Feeling No Pain

Zaux went to the guitar store to buy three items.All three items cost more than $0.99 and less than $9.99.He wanted to find the total cost before he had to pay for them,so he adds them up.Since Zaux took more pain meds today than he should have(on purpose) he multiplys instead of adds.However,he still gets the correct answer.

Given that the total number of cents he spent ended in 7,find the cost of each item.

(there are two solutions)

The Logic Class

Cam is teaching a class at Puzzlarian University. The class titled "Logic Problems: The Best Approach" is always popular with students and this semester is no exception. There is only one space left in the class and three students have applied. Each of the applicants is interviewed.

The last space is taken by a student who makes either three true or three false statements. One of the other two applicants makes two true and one false statement. The other applicant makes one true and two false statements.

Here's what they said during their interview:

Knightmare:
1. Curtis is the oldest
2. Karl will not bring the teacher an apple
3. I am the one with three true statements

Karl:
1. I would bring the teacher an apple
2. Curtis will be chosen
3. Knightmare's first statement is false

Curtis:
1. I am the oldest, so I should be selected
2. Karl will be selected
3. Karl's third atatement is true


Which student was selected as the last person chosen for the Logic class?

Some real groaners ...

1. What pudding makes the best cricketer?

2. Why was Moses the most wicked man who ever lived?

3. On what toe does a corn never form?

4. What is the difference in a hungry man and a glutton?

5. Why should turtles be pitied?

6. Why should young ladies set good examples?

7. Why should the male sex avoid the letter A?

8. Why is chimney-sweeping a very agreeable business?

9. Why is a joke less durable than a church bell?

10. Why is Ireland likely to become the richest country in the world?

Bonus: Why should you never tell a man to take a back seat?

Family Ties

At one table sat a father,mother,son,daughter,uncle,aunt,brother,sister,cousin,nephew and niece.However,there was only four people sitting at this table.

How can this be?

The Parade

At the conclusion of the Persian War, Athens decided to have a parade. They wanted the heroic soldier who led the charge during the last battle to lead the parade. However, there was a problem. Socrates was asked to find this soldier. After much investigation, he came up with three names. He located and questioned the three ... here are their comments:

A said:

1. I led the charge in the last battle.
2. I am clearly the choice to lead the parade.
3. C was in the reserve ranks during the battle.

B said:

1. C did not lead the charge during the last battle.
2. I am the logical choice to lead the parade.
3. I could keep time with the parade music very well.

C said:

1. I should be selected.
2. B would not be able to keep time with the parade music.
3. I was not in the reserve ranks during the last battle.


Socrates learns that one of the men made one false statement; one made two false statements; and one lied altogether.


Which soldier did Socrates select to lead the parade?

Starting point

Cam,a pilot,starts up his plane at the Buenos Aires airport.Neal,a stranded traveller,needs a ride.Neal says to Cam "I want to go to puzzlaria."Cam said "That's no problem,it will not be more than just a few miles off my route."

Since Puzzlaria can be anywhere in the world,what was Cam's destination?

Reducing random numbers

Pick a uniformly distributed random number between 0 and 1. Continue picking until you pick one that is larger than the previous one that you picked. What is the expected number of numbers you pick (including the one that ended the sequence)?

NB Expected means average.

Cubic resistor

A wire-frame cube is made of 12 resistors of resistance R. What is the resistance between diagonally opposite corners of the cube?

The Art Store Robbery

A Picasso painting was stolen late last night from the Puzzlarian Art Arena. Someone used a hammer to smash a rear window ... there was no alarm system because rarely is there crime in Puzzlaria. Four suspects have been questioned. One of them told the truth in all three of his comments. Another's comments were all lies. It is not known whether the other two told the truth or lied. Detective Chris determined that the break-in was committed by a single individual.

Amendment: All suspects were in town the night of the robbery

Their comments:

Knightmare:
1. I did not do it.
2. I was in Puzzletown when the crime occurred.
3. Cam is guilty.

Cam:
1. I am innocent.
2. Karl owns a large hammer.
3. Karl was seen near the store last night.

Karl:
1. I do not own a large hammer.
2. Knightmare and Cam are both guilty.
3. I went to bed early last night.

Curtis:
1. Only one of my statements is false.
2. Karl was out late last night.
3. I am innocent.


Who lifted the Picasso?

Some more wise men in peril

I am note sure if this puzzle has been posted on this forum before as I am new here. If so, please let me know and I'll remove it...

A group of 24 wise men falls into the hands of a savage tribe who decide to execute them. However, the chief is curious to see just how wise they are. A day before the execution is scheduled, he meets the group and says:

“I’ll give you one chance tomorrow to save as many of the group as you can. You will all be placed in a queue such that each man can see all the others ahead of him in the line. A red or black hat shall then be placed on your heads. None of you will be allowed to see the colour of your own hat nor of those behind you though you can see the hats of those ahead of you. None of you shall communicate in any manner by speaking, touching etc nor shall any looking back or sideways be allowed.”
“Starting from the back, each man will be asked ‘What’s the color of your hat?’ The addressed man can only answer either ‘red’ or ‘black’. If the answer is correct, he is free to go. Otherwise, he will be put to death and we’ll move on to the next person in the queue and so forth.”
“ANY violation of any condition will immediately result in execution of ALL OF YOU. Now you may retire to bed.”

The wise men have the whole night to talk freely and plan their escape. What would be the best strategy they could adopt?

The derivative needed for h1

The "trick" to an Ag Engineering problem was in solving for h1.

Given:
dh=3
bw=12
cr=4
cs=0.01
ss1=6
ss2=6
ss3=6
CF=1.5

ac=((bw^2*cs+2*bw*(dh-h1)*(1+cs*ss2)+(dh-h1)^2*(1+cs*ss2)*(ss2+ss3))/(2-2*cs*ss3))
ad=((cr^2*cs+h1^2*(ss1+ss2)*(1+cs*ss2)+2*cr*(h1+cs*h1*ss2))/(2-2*cs*ss1))
CF=ac/ad

Find h1: h1 is about 1.5.

There are several ways to find the true value of h1. I showed one in the solution to "An Ag Engineering problem".

But a good way would need the derivative of how CF changes with h1. I finally solved that. And with Newton's
method (also known as the Newton–Raphson method, the solution is quick and accurate.

Can anyone show the derivative or show a better method?

The Ethical Criminal

After being captured and put in jail, Jim had quite an effect upon the guards. They liked him so much, that one night his cell door was intentionally left unlocked. To the surprise of everyone, Jim remained in is cell. When asked why he did not escape, he said, "To quote Socrates, 'If you accept society's rules, you must also accept its punishments.'"

All the guards were questioned as to who left the cell door unlocked. Here are the comments:

Guard A:
1. I did not leave the door open.
2. C was the one who did it.

Guard B:
1. I was not on duty that evening.
2. A was on duty.

Guard C:
1. B was on duty that evening.
2. I hope Jim would escape.

Guard D:
1. I did not leave the door open.
2. I am not surprised that Jim did not try to escape.

Of the eight statements, only three are true.


Which guard left the cell door unlocked?

No More Anonymous Comments

Hey Guys

I have to restrict the Anonymous comments because I was getting a lot of spam.

You can still comment if you have an OpenID or a google account.

Regards
ToM

Fermat upside-down

The world-famous Fermat's Last Theorem states that the equation aⁿ+bⁿ=cⁿ has no integer solutions where n > 2. It was proposed by Pierre de Fermat in 1637, and was not proven until 1995, 358 years later, when Andrew Wiles proved it. It took over 100 pages for him to do this, and even then, he relied on others' work in elliptic curve theory over the previous forty years.

I have a much simpler theorem I want proved. Prove that the equation n^a+n^b=n^c has no integer solutions where n > 2.

Questions ...

1. What is the largest room in the world?

2. What is it that a man does not have, can never have, and yet can give it to a lady?

3. Why is a recently jailed person like a boat?

4. When does a ship tell a falsehood?

5. What is the difference between a mother and a barber?

6. Why are fowls economically beneficial animals for a farmer?

It's my mule!

Pingy, Ross, and Mohamed are three farmers in Puzzlaria. Their farms are closely located , and they often loan each other farm animals, and tools. A mule has been passed back and forth so many times, that actual ownership of the animal has become a question. Each farmer makes two statements, one true, and one false:

Pingy said:
1. "It is Mohamed's mule."
2. "It is not mine."

Ross said:
1. "It is not Mohamed's".
2. "It is Pingy's."

Mohamed said:
1. "It is my mule."
2. "Ross's 2nd statement is false."


Who is the owner of the mule?

The Poker Hand

In a five card poker hand:

∙ no card is above a 10
∙ no two cards of the same value
∙ all four suits represented
∙ total values of odd and even cards is equal
∙ no three cards in sequence
∙ black cards total 10
∙ hearts total 14
∙ lowest card is a spade


Name the five cards.

33^m - 7^n

If m and n are positive integers, what is the smallest absolute difference of 33^m - 7^n ?

The Bus Conversation

Pingy and Neal arrived at work in the Puzzlarian Puzzle Factory. Enjoying their first cup of coffee, the following conversation insued:

Pingy: "This morning on my bus ride to work, there were only three other passengers and I knew everyone on the bus. During the ride, one of them mentioned ages, and I mentally figured that the product of their ages was 2,450 ... and if I totaled the ages, the sum was twice your age. How old were the three passengers?"

Neal: "Wait a minute ... you haven't supplied enough information!"

Pingy: "Oh yeah, I forgot to tell you that one of the passengers was older than I am, which is ...."

Neal: "Yeah, I know how old you are. And now I also know how old each of the passengers were ... they were __ , __ , and __ years of age."


Complete Neal's last statement.

Also, how old are Pingy and Neal?

Missing Digit

Find the missing digit!

4,?,9,3,7

- Francois Joubert

Chris's English Comprehension Test

Old and Young's ages total 48 years.

Old is twice as old as Young was, when Old was half as old as Young will be, when Young is three times as old as Old was, when Old was three times as old as Young.


How old is Old?


(just reading that ... :) ... gives me a headache ...)

How many trains?

Around the perimeter of Puzzlaria, there is a circular railway with trains running in both directions. Trains run every 15 minutes each way. At 8PM, they each board a train, DualAspect heading in a clockwise direction around the city, and Ross heading counter-clockwise. Clockwise trains take 2 hours to accomplish one lap and counter-clockwise trains require 3 hours.

Including the train each one is riding on, how many trains did DualAspect and Ross see on their 1 lap trip around Puzzlaria?

An Elusive Idea

The concept of time has been bantered about by scientists, writers, and philosophers since man crawled from the ocean, climbed down from a tree, or had some sort of divine beginning. Although its progression is constant and continuous, sometimes, during stressful situations, it seems to slow to a crawl ... and pleasurable events often pass with the blink of an eye.

The elusive idea, or concept we are searching for, happens but once in a minute. It seems so insiginificant, we don't give it a single thought ... rarely, have I known anyone to focus on it. Yet, the concept of a moment, very similiar in nature to the minute, always enjoys a couple of these.

What is this elusive idea we seek?

Iron chain

A man has nine pieces of iron chain, with these sizes:

one 3-link chain

one 4-link chain

two 5-link chains

three 6-link chains

one 7-link chain

one 8-link chain

He wants to join them into one long 50-link chain, so he takes them to the hardware store. The store informs him that there is a $1 charge for cutting open any link, and a $2 charge for welding an open link back together. But he can buy a brand new 50-link iron chain for only $25. Is there a cheaper solution?

(This is based on a puzzle from a very old book by A. K. Dewdney. Now that I've finished writing it, I realize that $25 for a 50-link iron chain is insanely expensive. But go with it.)

Queue height

Some (n) people are standing in a queue. On average, how many of them can say that they are taller than everyone ahead of them?

NB The person at the front of the queue, can say that he is taller than everyone ahead of him.

Tavern Games

Puzzlarians love games. In the Puzzlarian Tavern, residents enjoy chess, darts, cards, pocket billiards, snooker, and word games. Chris and Kightmare are sitting at one of the tables, enjoying a cool beverage, and playing a word game.

The game involves a well known number sequence and the participants memory ability.

Chris begins the sequence by saying. "One".
Knightmare says, "One - two".
Chris says. "One - two - three."

The first 20 numbers in the sequence are:
1-2-3-2-1-2-3-4-2-1-2-3-4-3-2-3-4-5-3-2

Knowing that the 40th number is "2" ... who will be the first to say "10"?

Where's the Fifty?

Three envelopes lie on the table in front of you. In one of them is a fifty dollar bill. Each envelope has two statements written on it. One has two true statements; one has two false statements; and one has a true and a false statement. If you can logically determine which has the money, it is yours.

Envelope 1:
a) the money is not in here
b) the money is in envelope 2

Envelope 2:
a) the money is not in envelope 1
b) the money is in envlope 3

Envelope 3:
a) the money is not in here
b) the money is in envelope 1


Which envlope will make you $50 richer?

How old!!!???

A girl was eight years old on her first birthday. How could that be?

Who's crooked?

Consider a group of 100 politicians. Each one is either crooked or honest ... (jeez! can't believe I am suggesting that Venn diagrams of Honesty and Politicians might actually intersect ... oh well). You are given 2 facts:

a) at least one of the politicians is honest
b) given any two of the politicians, at least one of the two is crooked


Can you determine how many of the 100 are honest and how many are crooked? ... explain.

A Tougher Series

Find the missing number in the series:

3 - 11 - 20 - 27 - 29 - 23 - ?

What's her name?

Two girls have last names Billingsley and Jenkins. Not in a particular order, their first names are Sally and Susie. Two of the following are false:

Susie's last name is Billingsley.
Susie's last name is Jenkins.
Sally's last name is Jenkins.


What are the complete names of the girls?

Bonus question: How old are they if Sally has blonde hair? ... :)

Next number please ...

Next number please:

1 - 2 - 6 - 30 - 60 - 180 - 900 - 1,800 - 5,400 - ?

Last Digit

What is the last digit of 24784337^38383822458 ?

- Shpilo

very much alike! ...

The two number groupings below each have the same realtionship between the two numbers:

3 ... 8

-5 ... 24

0 ... -1

9 ... 80

6 ... ?

What is the missing number in the last grouping?

Monday Night Bowling

CJ and his team(The Head Pins)played two bowling games against another team(The Misfits).For the first game,all the players sat at three tables with the same number of people at each table.At the end of the first game,it was found that The Misfits were cheating and an argument broke out.During the second game(with the two teams mad at each other)The Head Pins sat at one table while The Misfits sat at another.During both games,everyone bought a round of drinks for the table they were at.But during the second game,38 more drinks were bought(in the same manner)than the first game.

What is the number of people on each team?

How many drinks were bought during each game?

(there are more than 1 person on each team)

Where do I sit? ...

Thirteen friends decide to go to the movies. In the theater, there are rows of 13 seats. For fun (or some stupid reason) they decide that the first person to enter the row may sit wherever he chooses. The second person must sit on either side of him with no empty seat between. The third person may sit on either side of the first two as long as no empty seat is between them. This procedure continues until all are seated.

Remembering that the first person may choose any of the seats, how many different seating arrangements are possible?

It's how hot?

As a new resident of Puzzlaria, Chris is not familiar with the two most commonly used temperature scales. The scales bear no resemblance to the Farenheit, Centigrade, and Kelvin scales with which he is familiar.

He is told by Ragknot that 14⁰ in the first system is equal 36⁰ in the second. Also he is informed that 133⁰ in the first is 87⁰ in the second.


What is the formula for converting one system temp. to the other?

At what temp. will both thermometers read the same?

3,2,1 blast off ...

Two rockets are aimed such that they will just miss each other. They are launched simultaneously. The rockets are programmed to land at each others launch point. They will travel the same distance ... horizontally and vertically. At the point of flight where the 2 rockets pass each other, one takes one additional hour to reach its destination and the other takes nine more hours.


How much is one rocket's velocity faster than the other?

Answer the phone ...

Cam tried to phone his wife all afternoon ... but she never answered. When he finally arrived home, she was gone, but this message was on the table:

←936←8 _←8→6 _28→9 _←2 _63←9 _←74→663


Cam looked at the code and said to himself, "Jeez, no wonder she didn't answer".


What did the message say?

No frills ... just Logic ...

Correctly associate each letter and number:

If A is 1, then B is not 3.

If B is not 1, then D is 4.

If B is 1, then C is 4.

If C is 3, then D is not 2.

If C is not 2, then D is 2.

If D is 3, then A is not 4.

How many sons

I. Mrs. Jones has two children. At least one is a boy. What are the chances that both are boys?
II. Mrs. Brown has two children. The younger one is a boy. What are the chances that both are boys?

Not the World Series, but ...

Find the missing numbers in these series:

1. 1 -- 9 -- 18 -- 25 -- 27 -- 21 -- ?

2. 1 -- 2 -- 4 -- 13 -- 31 -- 112 -- ?

3. 1 -- 4 -- 2 -- 8 -- 5 -- 7 -- ?

4. 9 -- 3 -- 15 -- 7 -- 12 -- ? -- 13 -- 5 -- 17 -- 11

5. 0 -- 2 -- 4 -- 6 -- 8 -- 12 -- 12 -- 20 -- 16 -- ?

6. 16 -- 21 -- 26 -- 26 -- 12 -- ? -- 19

7. 3 -- 4 -- 11 -- 16 -- 27 -- 36 -- ?


Hint: Some of the numbers may not be related mathematically ...

Four sheep

Farmer Giles has four sheep. One day, he notices that they are standing in such a way that they are all the same distance away from each other. How can this be so?

Kinda Corny ... :)

If 9 men and 7 women can pick as much corn in 5 days as 7 men and 11 women can pick in 4 days ....


Who are the better corn pickers ... the men or the women? ... and by how much?

Chewing Gum in Puzzlaria

Gum chewers comprise 78% of all the people of Puzzlaria.
People under the age of 15 are 35% of the population.


If you select a Puzzlarian resident at random, what is the probability that the person is not a gum chewer and above the age of 15?

Going home

A chauffeur always arrives at the train station at exactly five o'clock to pick up his boss and drive her home. One day his boss arrives an hour early, starts walking home, and is picked up by the chauffeur on the way out to the train station. They arrive at home twenty minutes earlier than usual. How long did she walk before she met her chauffeur?

Speak the Language

In Puzzlaria, many years ago, a secret language was developed. The language was used to communicate secret messages during war between Puzzlaria and Rationalica.
In the secret language:

"Kaf navcki roi" means "Take three pieces".

"Kir roi palt" means " Hide three coins".

"Inoti kaf kir" means "Cautiously take coins".


In the secret language, how would you say "Hide pieces cautiously"?

Business Meeting

Chris, Knightmare, Cam, and Karl are scheduled for their monthly business meeting. Their occupations are author, biologist, chemist, and doctor ... but not necessarily in that order. Karl just told the biologist that Cam was on his way with doughnuts. Chris is sitting across from the doctor and next to the chemist. The doctor was thinking that Knightmare was quite an unsusual name for parents to choose, but he kept the thought to himself.

What is each person's occupation?

Poor Fred

Fred lives alone in a small cottage just outside of Puzzlaria.Being lazy and not wanting to leave his couch,Fred had everything delivered to him.One Thursday, Peter came over for a visit and found Fred dead on the floor.On the porch,there was three bottles of milk,a Monday`s newspaper,a sears catalogue,charity flyers,Netflix movies,a prepaid pizza and some unopened mail.

And the killer is...

Powerful Remainder

Divide 7³³ by 10 ...

(if it's too small to see properly, it is 7^33)

What is the remainder?

That's not my hat ...

After a fun day at the Puzzlarian Picnic, several residents ended up at the Puzzlarian Tavern. At 2AM, the bartender had to ask the last six to leave. Chris, Cam, Knightmare, Karl, Ross and DualAspect had each worn a hat to the picnic that day. However, at 2AM, something had mysteriously blurred the vision of each one, and they could tell which hat each owned. Out of frustration, and the bartender's continuous requests that they go home, each grabbed a hat and left.

Not a single one of the guys grabbed his own hat.!


What is the probability of no one getting the right hat?

Gathering Potatoes

At the annual Puzzlarria picnic, there is lots of fun and games.
Scenario:
A basket, large enough to hold 100 potatoes is placed on the ground. Beginning 10 feet from the basket, and in a straight line, a potato is placed every 10 feet ... a total of 100 potatoes. A prize, of a night of free beverages at the Puzzlaria Tavern, is offered to the FIRST person who correctly answers the question:

If a person gathers all the potatoes, one at a time, and places them in the basket, how far would he or she travel? (for clarity, each potato gathered must be placed in the basket before gathering another)

Game:
Ross and Curtis were selected in a random drawing to participate in the POTATO GATHERING CONTEST. Because Ross is 2.04% faster than Curtis, he offers to allow Curtis to gather one potato and drop it in the basket before he begins to gather. For clarity, Ross will have to gather 50 potatoes before Curtis can gather his remaining 49. The results of the race will vary depending on which first potato Curtis gathers and places in the basket.

Which potato should Curtis gather first to increase his chance of winning, and if he chooses correctly, by how much would he win? (for clarity, each potato gathered must be placed in the basket before gathering another ... and there is only one line of 100 potatoes, 10 feet apart ... so each participant is gathering from the same line of potatoes)

Puzzlaria's Mayoral Election

Knightmare has run a splendid campaign and was elected the Mayor of Puzzlaria. 5,219 votes were cast for the four candidates. He beat Chris by 22 votes, Karl by 30 votes, and Ross by 73.


How many votes were cast for each candidate?

The Family's Age

One member of a family of three was celebrating a birthday. The boy asked a question about the ages of his parents. His father replied:

"Our three ages combined amount to seventy years. As I am just six times as old as you are now, it may be said that when I am but twice as old as you, our three combined ages will be twice what they are at present. Can you tell me your mother's age?"


How old is the boy's mother?

144

In what number bases does 144 represent a square number.

How odd!

Is the the number 124 (in base 5) odd or even? More generally, how can you tell if a number in any base, is odd or even? (Don't worry about the obvious issues for bases > 10).

32 card trick

Alfred, Brian, Christopher and Damon play with a deck of 32 cards. Damon deals them out unequally, then says: "If you want us to have the same number of cards, do exactly as I say. You, Alfred, divide half of your cards between Brian and Christopher. Then, Brian, you do the same with Christopher and Alfred. Finally, Christopher, you follow suit with Alfred and Brian." How did Damon distribute the cards?

They got married ...

Three young ladies got married on the same day. Their combined weight was three hundred and ninety-six pounds. Nellie weighed 10lbs. more than Kitty, and Minne weighed 10lbs. more than Nellie. Bridegroom John Brown weighed exactly the weight of his bride. William Jones weighed half again as much as his bride. Charles Robinson weighed twice the weight of his bride. All together, the 6 people weighed half a ton.


What was the full name of the three brides after the wedding ceremony?

The Barter System of Puzzlaria

The good residents of Puzzlaria often use a barter system to exchange goods and services. A fairly accepted equality is 85 chickens in exchange for a horse and a cow. Another accepted value is 5 horses for 12 cows.

Karl and Ross manage a small farm and are at the marketplace looking for livestock.

"Ross," said Karl, "I believe we should take as many more horses as we have already selected. This will gives us 17 horses and cows to feed through the winter."

Ross suggested, "I think we need more cows than that. If we double the number of cows we have picked, we would have 19 horses and cows ... and we would have just enough chickens for a fair trade."

How many chickens did Karl and Ross bring to the marketplace?

The Old Tower

Tower description:
1. 300 ft tall from ground to top of last step.
2. a circular handrail and steps lead from bottom to top.
3. there's one picket in the handrail for each step and they are 1 ft. apart.
4. the diameter of the imaginary cylinder which the handrail twines around is 23 ft. 10 1/2 inches.

The circular staircase has how many steps?

Evens and Square Numbers

Prove that adding up even numbers starting with 0 cannot addup to a square number
Ex. 0+2+4+6+8+...


OR


Show the square number it adds up to and its root

- Jordan McMichael

Four Quarters

Start with a square. Divide it into four equal square quarters. In the top left corner, draw the largest possible circle. Shade it in. Divide the three remaining quarters into four quarters. In the top left corner of each of those, draw the largest possible circle. Shade it in. Continue this process of division into quarters, and shading the top left incircle. What fraction of the square will be shaded? What is the significance of this number?

-Shpilo

An Ag Engineering problem

Cam solved an engineering problem last week. He did a great job. I’ll offer another. This is a diagram of a diversion, which is a very simple and common earth structure for diverting water. The question is to find the flow area (the area below the blue line). If the depth is less than 0.5 foot on the cross slope, the velocity is slow and not counted, thus the vertical blue line. The diversion height is 3 foot (-1.5 to +1.5), but there’s a 0.5 freeboard so the water depth is 2.5 foot. The cross slope (black line) is in percent, 100 foot horizontal to 1 foot vertical. The red slopes are 6:1 (6 foot horizontal to 1 foot vertical). For this section we want the cut/fill ratio to be 1.5. The amount of cut (blow black) is 1.5 times the fill area (above black line). The top width of the diversion is 4 feet and the bottom width of the diversion channel is 12 feet.

Note: The +1.5 and -1.5 was read from the graph, and are approximate. As you can see in the drawing the top is slightly above 1.5 and the bottom of the channel is slight above the -1.5
The exact difference is 3.000 however. Here's a hint. Lines pass through the origin to simplify the process. Moving the whole construction up or down is how the exact cut/fill ratio is obtained.

Question: What is the flow area? This is simple geometry, if you want to go further, then what is the amount of flow in cubic feet per second using Manning’s Equation, given other inputs?

Diversion


Inputs

Diversion Solution

Ragknot's Money

Ragknot went to a bargain sale in the Mall of Puzzlaria. He claimed half his money had been spent in 30 minutes. He said he was left with as many pennies as he had dollars before, and but half as many dollars as before he had pennies.

How much did Ragnot spend?

Grinding Wheel

The Wizard of Oz and Ross, both respectable residents of Puzzlaria, have each started small businesses in the basement of their homes. While walking one day, and enjoying a smoke of one of the strange herbs which grows wildly in the fields surrounding Puzzlaria, they see a yard sale sign.

One item for sale is a large grinding wheel, 22 inches in diameter, with a 3 1/7" bore. Neither has a particular use for it, but the price is right, so they split the cost and make the purchase. The flip of a coin decides that Wizard will be the first owner of the wheel. It is decided that once he uses half of the wheel, he will give it to Ross.

What will be the diameter of the wheel when Ross receives it?

(Amendment: wheel bore has been added)

It's how far?

Chris, favoring his injured leg, calls Knightmare and asks if Knightmare will let him ride his mule to the next village of Paradoxia. Knightmare agrees to the loan, but offers to walk along in front so his mule will see him and not buck Chris from its back ... besides, Knightmare knows the best route and tells Chris they will stop in Guessville for refreshments before continuing.

After traveling for 40 minutes, Chris asks, "What distance have we covered so far?"

Knightmare responds, "Just half as far as it is to Guessville."

After creeping along for seven more miles, Chris asks, "How far is it to Paradoxia?"

The reply, as before, was, "Just half as far as it is to Guessville."

They arrived at Paradoxia in one more hour of travel.


How far is it from their hometown to Paradoxia?

1,000,000,000!

How many 0s (zeroes) are there at the right hand end of 1,000,000,000! ?

That's one billion factorial ≈ 1.7 x 10^(20,723,265,847).

Sharing marbles

A group of children share marbles from a bag. The first child takes one marble and a tenth of the remainder. The second child takes two marbles and a tenth of the remainder. The third child takes three marbles and a tenth of the remainder. And so on until the last child takes whatever is left. Knowing that all the children end up with the same number of marble, how many children were there and how many marbles did each one get?

Dinner Party

DualAspect takes a break from his hang-gliding, sky-diving, and lion taming to host a dinner for several of his Puzzlarian neighbors. He decides to prepare a turkey for the get together, and visits the local butcher to purchase a bird.

As he enters the butcher shop, he sees a puzzle buddy Chris. He listens as the butcher explains pricing.

"The little birds sell for two cents a pound more than the big birds. As you can see, I have pulled two turkeys from cold storage ... together they weigh twenty pounds," said the butcher.

Chris offers to go by the Puzzlarian ABC and get beverages for the evening. Dual buys both birds ... paying 82¢ for the small bird and $2.96 for the larger.


How much did each gobbler weigh?

Leisure Time

Four residents of Puzzlaria, DualAspect, Ross, Curtis, and Ragknot, spend their Saturdays in leisure activites each one loves. The activities are:

boating
music
reading
golf

Each of the four residents spends a different amount of time in their preferred activity.

1. Neither DualAspect nor Curtis plays golf, or is the one who spends 3/4 of the day Saturday in leisure interests.

2. The one who spends 3/5 of Saturday in leisure interests does not like boating.

3. The one who spends .9 of his day Saturday in leisure does not enjoy boating or music.

4. Ragknot does not play golf, nor does DualAspect enjoy reading.

5. The one who enjoys boating is not the one who spends half of the day Saturday in leisure interests.

6. Ross does not spend .9 of his Saturday in leisure interests.

7. The golfer does not spend half of his Saturday in leisure interests.


Which of the Puzzlarians mentioned, enjoy which leisure activity? ... and how much time do they devote to it?

Bad Knee

Karl and Ross were in a 100 meter race.When Ross crossed the finish line,Karl was only at the 90 meter mark.The red faced Karl blamed his trick knee for the loss.Ross laughed and said "in that case,let's have another race.This time I will start 11 meters behind the starting line."

All being equal,who will win the race?

Puzzlarian Golf

The small country of Puzzlaria has recently completed construction of its first golf course... called the Problematic Hole. Four residents decide to give the new course a go. Ross, DualAspect, Karl, and Knightmare met at the first tee and began the round.

At the end of the round, their caddies were heard making the following comments:

1. The player with highest score did not lose the fewest or the most balls.
2. The one with the second lowest score, who was not Knightmare, did not lose more than three balls.
3. The player with lowest score did not lose four balls.
4. The one with highest score lost more than two balls.
5. DualAspect did not lose more than three balls or fewer than two balls.
6. The player who lost only one ball was not the one with the lowest score.
7. Neither Knightmare, who was not the one with the highest score, nor Ross, lost more than three balls.

What was the scoring order, from lowest to highest? ... how many balls did each player lose?

You're How Old?

Five residents of Puzzlaria, Chris, Karl, Knightmare, Curtis, and Ross, are employed as Airfoil Technician, Communications Consultant, Space Planner, Lunar Energy Engineer, and Synthetic Food Nutritionist. They were having drinks at the Problematic Tavern. The waitress, attempting to be clever, asked if everyone at their table was old enough to order alchoholic beverages.

The bartender, who was walking by the table, interrupted, "yeah, I know these guys ... they are of age to purchase". He continued:

"The Communications Consultant is not younger than any of the other four. Curtis is not as old as Chris and not as young as Karl, who is not as old as the Lunar Energy Engineer, but not as young as Knightmare. The Airfoil Technician is not younger than the Space Planner, who is not younger than the Synthetic Food Nutritionist. Knightmare is not the youngest of the five ... and no two are the same age."

How is each Puzzlarian at the table employed?

Little piggy's bank

If it has a 5 inches x 4 inches base and height of 11 inches, how many standard sized pennies can you put into an empty piggy bank?

Word Equations

You are probably familiar with word equations that work something like this:
29 = D in F in a L Y
This works out to 29 = Days in February in a Leap Year. Can you solve the 10 equations given below in a similar manner?

1.) 40= T with A B
2.) 20 = M T in H C
3.) 3 = W M in H B
4.) 17 = N of S in a H
5.) 5 = V in E A
6.) 33 = V in H S
7.) 7 = Y I
8.) 12 = E on a C
9.) 7 = D with S W
10.) 17 = S in a G (H P)

You Live Where?

In the densely populated country of Puzzlaria, it is a law that residences must be at least 6 story buildings to accomodate more people. The following Puzzlarians live in the same building:

Chris
Cam
Knightmare
Karl
Ragknot
Curtis

In Puzzlaria, most Puzzlarian comments seem to be puzzling, and also not very clear... ;-).
When a visitor asked on which level of the building do they reside, the building manager stated the following:

1. Chris does not live above the third level.
2. Neither Knightmare nor Ragknot lives above either Karl or Curtis.
3. Curtis does not live below Chris or Cam, and does not live above Karl.
4. Ragknot does not live below Cam or above Chris.

What a puzzling situation ...

On what level of the 6 story building do these Puzzlarians reside?

words

Which word from group B belongs with the words from group A?

A:blast,paper,box

B:juice,carpet,hat,bag,boat

How long the palindrome?

As you know, a palindrome word is one which reads the same forwards or backwards.
Examples:

reviver
repaper

What is the longest common English palendromic word?
Is there one longer than 7 letters?

Relationship

Albert Wells introduced James Cole to his friend as his 'Uncle James'.Likewise,James Cole introduced Albert Wells as his 'Uncle Bert'.One of they're friends said"If you are uncles to each other,you must be nephews to each other as well."

How can this be correct?

World Travelling

For fans of QI, you'll know this....

What is the shortest time to theoretically get to anywhere on the planet? And how would you do it?
Whilst you may assume it would only take but a moment to move to just over there..... how long would it take to get to the furtherst point on the globe? The answer is fascinating, and impossible, hence theoretical, but could be done on the moon.... Bonus points if you know how long it would take on the moon....

- Karl Sharman

Sons or daughters?

While walking in a park you encounter an old friend from times gone by. He invites you immediately to dinner to do some catching up.

Between courses you need to use the bathroom, and you enter the hallway upstairs. The door you thought was the bathroom seems to be something else: Completely pink, dollhouses, toys etc. Some girls bedroom.
The next door you try was correct. On your return to the dinner, you notice an envelope lying on the doormat. You recognize it as a letter sent to parents of at least one boy, to advertise some summer camp.


Back at the table, your friend shares that he has in fact three children.

The question is: is it more likely that he has two boys and one girl, or two girls and one boy? Can you figure out the exact probabilities?

4 missionaries in peril

Hi guys, I'm new to the site, and haven't finished reading through the complete archives. This makes it possible for me to post a well known riddle. In this case: just shoot it down!

In a world full of mysterious hypothetical civilizations, 4 happless missionarries stumble uppon a village of ferocious cannibals. The cannibals however, always give their prospective meals a chance to escape.

The missionaries are ordered to stand on a small stone pyramid and must remain completely still. Any unauthorized movement will result in their swift end. They are positioned as on the following diagram:



The small v's coming out of the heads, represent their viewing direction. As you will have noticed, two are wearing white hats, while two are wearing black hats. The explorers are made aware of this, but cannot know their own colour.

The missionaries are free to go if only one yells out his own colour. No mistakes are allowed. No retries.

How is this possible?

Mow the Lawn

A man begins to mow his lawn which is 100 feet by 100 feet. The lawn mower has a 36 inch cut and the man mows around the outer edge, working closer to the center on each successive lap.

After which lap, will the mowing be the closest to being half finished?

Family planning

My mother dreamed of having nineteen children. Her dream didn't come true. But I have three times as many sisters as first cousins, and I have half as many brothers as sisters. How many children did my mother have?

It's all not true.

1111 - 22

Here's a fairly straightforward one:

Consider the sequence of numbers: 11-2, 1111-22, 111111-222,...
Show that they are perfect squares. What else do you notice?

Six take a test ....

Six student are sitting in a row of seating with an aisle on each end. The professor has instructed that students may leave as soon as they finish the examination.

If they finish in random order ... what is the probability that a student will have to pass by one or more students when exiting the row of seating?

3 x 3 colors ...

Consider a grid sized 3 x 3. Using three colors, red, white , and blue, (to color the cells in the grid) ... how many distinct patterns can be displayed if all three colors must appear in every column and every row?

Ghost Office --- LOL

Since now both Vampires and Ghosts both get their mail at the Ghost Office,
the Ghosts complained about having to go shoulder to shoulder with those Vamps.

The Ghost Master then told the Ghosts that from now on, they should pick up their
mail from a special department. What was the department's name?

There is a difference ....

One of the words below does not belong:

contest
mark
wind
bass
project
entrance
desert
record
console
content

Which one? ... why?

Symbols

Replace the question mark with the last symbol in the sequence ...

Since you can't draw it very well .... you can describe what the symbols mean and describe the next one.

Phone Message

Letters associated with numbers on a telephone:

- 2------3-------4--------5-------6-------7-------8--------9
ABC---DEF----GHI-----JKL----MNO---PRS----TUV----WXY

Complete the sign below which is in an optometrist's office:

? ? ? ? ---- ? ? - - - ? ? ? ---- ? ? ? ? ----- ? ? ? --- ? ? ? ? ----- ? ? ? ?
8 4 4 7 -- 4 7 ---- 8 4 3 --- 7 4 8 3 --- 3 6 7 -- 7 6 7 3 --- 3 9 3 7

Pain Meds

Zaux is on two types of medication.He must take one pill A and one pill B a day.He has to be careful not to take any more than one of each per day,as it would have side effects that will make him loopy.He can not take pill A without pill B,or vise versa, as this will also send him to la-la land.One morning, Zaux opens pill bottle A and taps out one pill into his hand.Grabbing bottle B, he does the same but by mistake, two B pills fell into his hand.

Looking down at the three pills,he can not tell them apart.They look alike in every way.He thought about it for a while,then did something which give him the correct dose.

What did Zaux do?

1 thru 6

Using the digits 1,2,3,4,5 and 6 only once,can you fill in the blanks?


??*?=???

The Word

In the following sentences, you are looking for one word to fill in both blanks in the sentence. The word, will obviously have the same spelling in both instances, but may have the same or a different pronunciation, and will have a different meaning.

Example: The archer will BOW before aiming his BOW at the target.
In the first instance of BOW, the meaning is a "gesture of respect". The second instance is referring to a "weapon".

1. She shed a ____ over the ____ in her expensive evening gown.

2. A ____ is a ____ portion of an entire year.

3. He ____ a rope around his leg to stop the ____ from bleeding.

4. It was easy to ____ class because student ____ was excellent.

5. The farmer was able to ____ better ____ than anyone else.

6. The ____ ____ to the rescue of its hatched babies.

7. He was in the ____ helping to carry the statue that seemed to be made of ____.

8. The ____ of ____ means not to speak.

Complete the Sequence

As the title suggests, complete the sequence:


2 -- 3 -- 6 -- 7 --_ -- 9 -- _ -- _ -- 8

After completing, EXPLAIN.

Red or blue

Three intelligent women, Alice, Barb and Carol, sit down to try out a test in logical reasoning. They are so arranged that each can see the color of a label which is either red or blue, attached to the hats worn by the other two but none of them can see the color of the label attached to her own hat. They are told that at least one of the labels is red. If any one of them can logically deduce the color of the label on her hat, she is to declare it. Carol decides to play this game with her eyes closed, knowing that the other two women have their eyes open. After a little time Carol, who has not seen the label on any of the hats declares her label colour. What is Carol's label colour (and why)?

This little piggie ...

A farmer owns pigs. He has 3 pink ones, 4 brown ones, and one black one. How many of the farmers pigs can say they are the same color as another pig?


(this sounds familiar ... hope I haven't posted it before ... if someone recognizes it as having been previously posted, advise and I will delete it)

Riddles

What do they mean ...?

1. What does a duck does when it flies upside down?

2. If all cars in the United States were pink, what kind of flower would the United States be?

3. How do you keep a skunk from smelling?

4. What did George Washington say to his men before they got in their boat to cross the Delaware?

5. Why does Tony the fireman have red suspenders?

6. What's big, green, and loves hot tamales?

7. Where do vampires get their mail?

8. What's Smokey the Bear's middle name?

9. What do you get when you cross a hippo with a jar of peanut butter?

10. What's gray, has four legs, a tail, and a trunk?

Bonus: Where does a 500lb. gorilla sleep?

Cross section 4+50

Talking about "Real Problems" I thought this might be
interesting. Below is data that will plot two lines, that
are plans for a dam to be constructed. The first of each
data point is an elevation (feet), the second is the distance
(feet) from the dam center line. Negative distances are on the
left. So these are y and x when plotting. The survey is
taken before the design, of course. Then from the design
we get a template to overlay the survey. The next step
is to compute the dam cross section area and the centroid
of the area.

1. What is cross section area?
2. What is the (Elev, Dist) centroid?
3. What we use would the centroid for?

Survey
Station 450
========================
687.05___-136.98
680.43____-61.62
677.47____-29.93
676.04______0.00
675.44_____18.60
671.13_____31.57
664.73_____58.17
661.83_____90.89
657.3_____103.84
654.79____113.55
658.54____129.44
662.13____140.12
663.34____165.83
=====================
Dam Template
680.92___-67.23
700.00___-10.00
700.00_____0.00
700.00____10.00
678.00____76.00
678.00____96.00
662.27___143.18

Table mat

Feb 12, 7:05 PM. I've rephrased the question completely.

A table mat is made from red and white beads. There is an inner rectangle made entirely using white beads. It has a border (on all four sides) made from a single layer of red beads. Which mats can have as many white beads as red beads?

Next

What's the next term in the sequence: 77, 49, 36, 18, ... ?

Generations apart

A woman and her grandson have the same birthday. For six consecutive birthdays, she is an integral multiple of his age. How old is the grandmother at the sixth of these birthdays?

3D diagonal

What is the length of the diagonal of a 3D rectangular prism (a cuboid) whose surface area is 94, if the sum of the lengths of the sides is 48?

Practical Problem

There's a long movie on TV this weekend and we want to tape it. The movie is well over two hours, but we only have a T-120 VHS cassette to use.

Here's the plan: we can record the boring beginning of the movie at slow speed (EP), and AT A CERTAIN POINT IN TIME we then switch over to the higher quality faster recording speed of SP. That way the whole movie will exactly fit onto one VHS cassette.

The problem is to find the algebraic expression that tells us exactly where that CERTAIN POINT is when we are to switch the recording speed.

- MikeO

Rhyme this ....

Pick words which rhyme with the words below so that the selected words form a meaningful sentence:

Whiff zoo bet kiss tour gritty yarn could.

What is his Birthdate?

In the year 1937, a man claimed he was x years of age in the year x². He also stated that if you add the number of his years to the number of his birth month, the results is the square of the day of the month in which he was born.

What's his date of birth? (month, day, and year)

a triangle's area

if you got a triangle which sides squares are 74, 116 and 370, can you figure out the area of the triangle?

word-summing

CHESS
CASH
BOWWOW
CHOPS
ALSOPS
PALEALE
COOL
BASS
HOPS
ALES
HOES
APPLES
COWS
CHEESE
"C.H."SOAP (<- just take this as CHSOAP)
+ SHEEP
_________

ALLWOOL

Each letter stands for a digit, find out, which.

tricky digits

How is it possible to write down 5 uneven digits, that make summed up 14?

A master of putting

A golfer is a real pro in putting, he can play the bal however he likes, but only in ranges of exactly 1, 5, 7 or 11 meters.

If he plays the ball farther than he is away from the hole, the ball rolls over it, eg. if he plays the ball from 4 meters away with a distance shot of 5 meters, the ball stops 1 meter behind the hole.

So if the ball lies 20 meters away from the hole, what is the minimum amount of shots to put the ball in the hole?

Reconstructed Division

Replace the "x"s with the correct numbers:

Man and Horse

There is a man and his horse. The man leaves town on Sunday, spends one night in a different town, he wakes up and returned home on Sunday .

How is this possible ?

- chw 1980

A Chris Special

Find the maximum and minimum values of (x^2 -2x + 2)/(2x-2) without using Calculus!

Ten Timer

A woman from New York married ten different men from that city,yet she did not break any laws.None of the men died,and she never divorced.How was this possible?

One Sentence

What is so unusual about the sentence below?(aside that it dosen't make a lot of sence)

"Jackdaws love my big sphinx of quartz."

Time to Check the Antifreeze?

Your vehicle has a radiator with a 21-quart capacity. It is filled with an 18-percent alchohol solution. How many quarts must you remove, to add enough 90-percent alchohol solution, such that the resulting solution contains 42-percent alchohol?

Weighty problem

You have goods to sell whose weights are whole numbers of kilograms, between 1 and 80. Using only 4 weights, what do they need to be?

Take your time

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later. What time is it now?

If I lived here, I'd be home by now!

If I drive half-way to my house at 30 mph, how fast do I have to go for the rest of the way to make the average speed for the entire journey of 60 mph?

Buying a rope

A man wants to buy a rope and so he goes into a shop. The shopman tells him that he has only ropes with a lengh of 100 feet for 20 cents each foot

The man tells him to cut off 20 feet of one 100-feet rope and sell it to him. The shopman measures the 20 feet with a 1 yard staff, but the man notes that the staff is 3 inches too short as it ends at the 33 inch mark.

After the shopman cut the rope off he said: „i changed my mind, I want to buy the 80 feet.“, so he gave him a 50 dollar note, but because the shopman couldn't change it he went to the neigbour shop to change the note and gave the change to the man, but he didn't knew, that the note was counterfeit so he had to displace it to the neigbour shop

So how many money did the shopman lost at all?

(sorry for my bad english)

Charming Inscription

This charming inscription is carved into a stone tablet, and sits above my throne (euphemism for toilet)

What does it say?

NUFSURO
RSETSYT
AERHETS
ETEAHEI
LOWTCAH

- Karl Sharman

Helix

You have a cylindrical tube, 9 inches long, with a 4 inch outside circumference. Ten turns of a wire are helically wrapped around its total length and secured at the ends.


How long is the wire?

Coffee or tea?

I have a cup of tea and a cup of coffee. I take a teaspoonful of tea and add it to the cup of coffee; stir briskly; then take a teaspoonful of the mixture and return it to the cup of tea, and stir that briskly.

After I'm done, there is:

(a) more coffee in the teacup than tea in the coffee cup
(b) less coffee in the teacup than there is tea in the coffee cup
(c) exactly the same amount of coffee in the teacup as there is tea in the coffee cup

Buying Flowers

Knightmare decides to buy his couch some flowers for Valentines Day ... (hmmm ... must be the little voices he hears ... oh well). Thinking it is tea, he accidentally consumes a large quantity of bourbon ... then heads to the florist.

He buys x number of flowers for y dollars (x and y are integers). As he staggers ... ooops, I mean walks away from the counter, after paying, the clerk says "If you buy ten more flowers, I will give you all for $2.00, and you will save $.80 a dozen". (the little voice says "don't do it").


How many flowers will Knightmare present to his lovely couch on Valentines Day? ... and how much did he spend?

Two Cylinders Meet

If the axes of symmetry, of two 2-inch right circular cylinders intersect at right angles:

What volume do the two cylinders share?


[some of you, who have more recently visited a classroom, may visualize this intersection ... I'm having trouble seeing it ... :-) ]

Losing at Tennis

In a single elimination tennnis tournament, there are n number of players. To determine a tournament winner ...


How many matches must be either played or defaulted?

Four Unknowns

Solve this system of equations:

x + y + z + w = 10

x^2 + y^2 + z^2 + w^2 = 30

x^3 + y^3 + z^3 + w^3 = 100

xyzw = 24


(brute force acceptable ... however, as Chris would say, "the method is much more interesting")

Movie Seating

Four couples decide to go to the movies ... at a small theater where each row has only eight seats.
The couples are:

Betty and Jim
Alice and Tom
Gertrude and Bill
Sally and Bob

Betty and Jim refuse to sit next to Alice and Tom.
Alice and Tom don't want to sit next to Gertrude and Bill.
Sally and Bob won't sit next to Betty and Jim

How can they be seated on the same row and satisfy everyone?

Grandchildren

Everyone of my grandchildren is under the age of eighteen. All of my granddaughters are very beautiful. My grandchildren all have red hair and blue eyes. The oldest grandchild has very long red hair. Twenty-one is the legal voting age.

Using the given information, how many of the following statements can be proved?: [state which one(s)]

1) My oldest grandchild may not yet vote.

2) My oldest grandchild is a beautiful girl.

3) My youngest grandchild may not yet legally drive.

4) My youngest grandchild has short red hair.

A Wordy Sequence

Here's a sequence of words:

APE --- BIRD --- CAN --- DIG --- EAT

Logically, which of the following could be next in the sequence?:

1. MAN

2. HAT

3. CAR

4. SEA

5. FIG

Out To Sea

400 years ago,a band of explorers were setting out on a sea journey to the far north which would last for three months.They had planned a celebration dinner of roast lamb for when they arrived.The problem was keeping the meat fresh for the three months.If they tied a rope to the meat and trailed it in the cold water,predator fish would eat it.If they took ice with them to keep the meat cold,the ice would melt and the ship would fill with water.

How can they keep the meat fresh for three months using what they had 400 years ago?

The Picky Dinner Party

You have invited the following people to a dinner party:

Sally
Mary
Steve
Alice
Jim

Being a person, who plans ahead, you have already purchased food items for the party. Three days before the party, you begin to receive phone calls informing of certain foods which the invitees can not eat. One day is left before the event, and you have received the following from your apparently "picky" invited dinner guests:

Mary won't eat fish or spinach
Sally won't eat fish or green beans
Steve won't eat shrimp or potatoes
Alice won't eat beef or tomatoes
Jim won't eat fish or tomatoes

Pretty disgusted with all the eating restrictions, you sit and analyze the foods you already purchased:

green beans
roast chicken
creamed codfish
celery
roast beef
lettuce

Of the food you purchased, what can you serve to appease everyones diet peculiarities?

A Sloom

All slooms have soft pits ... all gloops have hard skins ... all slurps are juicy. Some slooms are red ... some gloops are blue ... all slurps are yellow. Some gloops are yellow ... and some slooms are yellow.

Based of the given, which one of the following do you know about a sloom?:

1. It is red.
2. It is juicy.
3. It has a hard skin.
4. It has a soft pit.
5. none of the above

The Elusive Riddle

It can be short.
It can be long.
If you think it has weight,
You are definitely wrong!

It can't be heard.
It can be seen.
For heaven's sake,
What do I mean?


What is it?

De+syph+ur These!

Reveal these 12 words:

1. LFN+t

2. U+la+G

3. M+ba+C

4. X+10+d

5. b+AB

6. LMN+t

7. NM+a

8. X+ta+C

9. XQ+s

10. U+4+ic

11. XC+d

12. NV+us

Sports Anyone?

These sports are listed in what order?:

golf
tennis
baseball
softball
bowling
soccer
basketball

Superstitious?

Indentify these superstitious expressions:

1. causing the fracture of a brittle reflective surface

2. taking the extremity of an appendage of a burrowing animal with you

3. to move on foot beneath a climbing device

4. displaying a quadraped's hoofwear on a vertical surface

5. your intended walkway being traversed by a feline of the darkest color

6. to come upon a plant with foilage that is abnormal

It Means ...

Identify these popular sayings:

1. It is impossible to evaluate published matter by recognition of the material enclosing such matter.

2. That quality appealing to the senses extends as far as the epidermis layer.

3. The commodity used as a medium of exchange is to be positioned at one's oral orifice.

4. Performed activity verbally communicates at an audible level substantially more intense than the individual sounds of a language.

(easy, but fun)

Occupations

Somtimes a name or nickname sounds like a word whose meaning is associated with an occupation. Example: Banker -------> Bill

1. lawyer ---------------> ?
2. illustrator ----------> ?
3. thief -----------------> ?
4. disk jockey ---------> ?
5. athletic teacher ---> ?
6. barber --------------> ?
7. fisherman ----------> ?
8. baseball player ----> ?
9. nun ------------------> ?
10. meteorologist -----> ?

A Ragnot Special

A H H A A H / J O K E = H A


What is the arithmetic division?


(for this one, I have a solution, but no method)

Intersecting Circles

In the diagram below, the radius of the larger circle is 20 and the radius of the smaller circle is 15 (not drawn to scale). The illustrated radii are at right angles.

What is the difference of the areas of the non-overlapping portions?

Remove the Coin

Chris and Knightmare are enjoying a bottle of red wine from the StanLake Park Wine Estate. As the last glass is poured, Knightmare stands from the COUCH, reaches into his pocket, and pulls out a small coin. He drops the coin into the bottle and re-installs the cork.

Knightmare says, "Chris, I bet you another bottle of wine, that I can remove the coin from the bottle without removing the cork."

Chris exclaims, "Certainly, you can ... simply break the bottle."

"I can do it without breaking the bottle," Knightmare boasts.

"You've got a bet."


Could Knightmare actually remove the coin without compromising the structural integrity of the bottle? If so, how?

Window Cleaning Squeegies

You become employed with a large window cleaning company. The boss gives you $100, the address of the supply house, and instructs you to buy exactly 100 squeegies ... and you must spend all the money. He gives you the company tax number so that sales tax will not be charged.

When you arrive at the supply house, you are perplexed. There are three different squeegie types ... the supply house manager tells you the company you are representing ususally buys some of each type. The red ones cost $6.00 each ... the yellow ones cost $3.00 each ... and the blue ones are $0.10 each.

How many of each squeegie should you buy? ... remembering that the entire $100 must be spent ... and that you must buy some of each type.

A Tombstone

On a tombstone:

One sixth of his life was spent in childhood
One twelfth as a teenager
One seventh of his life passed from becoming an adult 'til marriage
A son was born in five years
His son died four years before him
He lived twice as many years as his son

At what age did he die?

1000 Lockers

A new princial arrived at the school to which he had been asigned. In a seemingly senseless act, he came up with a plan to begin to exert his authority. The school had 1000 students and 1000 lockers, which were in a single long hallway. After gathering all the students in the school auditorium, he presented his exercise in control.

He instructed the students to leave the auditorium in single file and head to the locker hallway. The first student was instructed to begin with the first locker and open every locker door. The second student was instructed to close every second locker. The third student was told that upon approaching the third locker, if it is open, close it ... and if it is closed, open it ... and then continue. The fourth was given the same instructions as the third student, except he was to begin with the fourth door. Each successive student was given the same instructions, which were obviously dependent upon his position in the line of students.

After the last student opened or closed the appropriate locker doors, how many remained open?

Unusual Dice Game

During a game of dice, a spectator decided to keep track of the rolls. He decided to track the product of the rolls. For example: a roll of 4 and 5 is scored as 20.

1st roll score - (we do not know)
2nd roll score - 5 more than the 1st roll score
3rd roll score - 6 less than the 2nd roll score
4th roll score - 11 more than the 3rd roll score
5th roll score - 8 less than the 4th roll score

Can you provide the numbers rolled on each of the five rolls?

Easy one

What's the next letter?

o-t-t-f-f-?

(just for fun)

Another Clock

Fred has a clock that chimes the appropriate number of times to indicate the hour,as well as chiming once at the half hour.As Fred walked into his house one day,he heard the clock chime once.A half hour later it chimed once.Still,a half hour later it chimed once,and a half hour later it chimed once again.What time was it when Fred got home?

Sam's Birthday

Little Sammy was 8 years old, two days ago. He will be 11 years old next year.

How is this possible?

Burn the Bridge

Four adventureres are being chased by a tribe of savages. They come to a very old rope bridge which crosses a ravine. They determine they have a 17 minute advantage over their pursuers. The rope bridge is weak and will only support 2 people at a time. To further complicate matters, it is dark and each crossing will require use of their only flashlight, to insure good footing. The bridge is too wide to allow the flashlight to be thrown across. The 4 adventurers, being of different age and levels of fitness, move at different speeds.

Adventurer A can cross the bridge in 10 minutes
Adventurer B can cross the bridge in 5 minutes
Adventurer C can cross the bridge in 2 minutes
Adventurer D can cross the bridge in 1 minute

How do all 4 adventurers get across the bridge in 17 minutes? ... so they can set fire to the bridge and assure their safety from the savages.

(amendment: when 2 adventurers are crossing together, they can move only as fast as the slower one)

Another Fork in the Road

Continuing on your journey to see the wizard, you come to another fork in the road. At this juncture, stand 3 men ... all looking wise and wizardly. Again, there is a sign ... it reads:

ONE OF US TELLS THE TRUTH, ONE OF US LIES, AND ONE OF US MAY
DO EITHER
(each of us knows which one is truthful, which one is the liar, and which one waffles between the truth and a lie .......... travelers may ask one of us, and only one of us, one question whose answer is either "yes" or "no")


What question would you ask to determine which of the roads you select, to continue your journey?

How Many Flowers?

All of Sally's flowers, except two, are roses.

All of her flowers, except two, are tulips.

All of her flowers, except two, are daisies.

How many flowers does Sally own?


(there are 2 possible solutions)

Who is the tallest?

(guys, this one drives me crazy ... and it was a fairly short trip ... :) )


In a rectangular array of people, who is taller?

* the tallest of the shortest people in each column

or

* the shortest of the tallest people in each row

Buses

Five buses are traveling along a road.The two in the front and the two in the rear are holding a total of 84 people.The middle bus has four people less than the average of all five.How many passengers are in the middle bus?

Which Way?

You're off to see the wizard ... the wonderful wizard of ... uh ...ok ... forget that. You are on a journey and come to a fork in the road. Standing there at the fork are two wizardly looking gentlemen ... ok .. they may not be gentlemen, but they are standing there. A truthful sign is on a post mounted in the ground next to the two men. The sign reads:

ONE OF US IS A TRUTH TELLER ... THE OTHER IS A LIAR
-------- Travelers may ask one of us ... one question ---------

What question do you ask, to obtain the correct information concerning the correct road upon which to continue your journey?

Game Show

You are on a game show and have the option of selecting 1 of 3 doors ... behind one of the doors is a fabulous prize ... behind the other 2 doors are gag gifts. The show host knows which door conceals the good prize.

You select a door. The host opens one of the other doors and shows you a gag gift. He now inquires if you would like to keep the first door you picked, or change to the other unopened door.

Should you keep the door you picked ... or change doors ... or does it matter?

(guys, I searched and did not find this puzzle ... If one of you recognizes it as having been a previous post, please advise and I will delete ... thanks)

Back to your roots

Evaluate rt(1 + rt(7 + rt( 1 + rt(7+......)))), where rt means square root. I have designed this so that the answer is an integer.

The Pop Bottle

The bottom 3/4 of a pop bottle's total height is cylindrical in shape.

The upper 1/4 of the bottle's total height is irregular in shape and glass thickness.

The bottle is filled with rum up to (approximately) the halfway point of it's height.Keeping the lid on and using nothing but a ruler,how can you tell what percentage of the total volume of the bottle is filled with rum?

Simplify

Simplify:

(27+8i)/(3+2i^8)

Submerge The Ball

Suppose you have a very large steel box that is open topped.It measures 50 feet x 50 feet x 50 feet.Inside this box is a steel ball-bearing that has a diameter of 42 feet.If you started filling this box with mercury,how many cubic feet would you have to pour in, in order to completely submerge the ball?

Raindrops keep falling on ... wait, wasn't that a song?

Which falls faster ... large raindrops ... or small ones? ... and why?

Baseball Toss

If you are holding a baseball ... and you toss it straight up, will the upward flight or the downward flight take longer? ... and why?

Bet it all on red ... oh wait...maybe black ...

Roulette has been called the "king of casino games". The very first primitive roulette wheel was designed, in the 17th century, by Blaise Pascal. Mr. Pascal was actually working on a perepetual motion machine when the idea came to him. The current version of the wheel was designed in France in the 18th century and had 36 slots in which the ball could lodge. Francois Blanc supposedly made a bargain with the devil to obtain the secrets of the roulette wheel ... this legend cam about based upon the fact that there were originally 36 slots ... 1 to 36 totals 666, the sign of the beast. Eventually european wheels came to use 37 slots and American wheels use 38.

One may wager:

a bet on a single number (the highest payout and least chance of winning)
a bet on a range of numbers
a bet on either black or red
or a bet on odd or even

Gamblers have devised and attempted many systems to use at the roulette wheel ... many have short term success, but the wheel will win if you play long enough ... unless, you know the SECRET.

What is the secret for guaranteed winning, during extended gambling sessions, at the Roulette Table?

Twice the Size

During your sleep last night, a space alien visited, from the planet Jumbo. To amuse himself, he used the enlarge setting on his space ray, and doubled you in size. When you awakened the next morning, you were shocked to find yourself twice as tall, twice as wide, twice as thick, and so forth. You smiled when you realized that, at least, your feet didn't smell twice as bad ... heh heh.

By how much did your weight increase?

Share the driving

Zaux and Cam took turns driving on a round trip using the same route both ways.Zaux drove the first 40 kilometers and then Cam drove the rest of the way.Zaux started to drive on the return trip and then Cam drove the last 50 kilometers.

who drove more and by how many?

setting the time

The only timepiece that Chris owns is a grandfather clock which he frequently forgets to wind.
One day when this happened,he went to Zaux's house to check the time.When Chris return home,the first thing he did was set the grandfather clock to the correct time.How could he do this if he didn't know how long it would take him to get to Zaux's house and back and he didn't use a radio,phone,etc.

Ball on an Inclined Plane

Place a ball at the top of an inclined plane (a wedge). Release the ball and allow it to travel for one second, stop it. Mark the distance it traveled on the plane. Measure the distance traveled and divide the remainder of the plane surface into segments equal to the distance the ball traveled in one second.

Perform the same experiment 4 more times, how many segments will it travel in:

2 seconds -> ?

3 seconds -> ?

4 seconds -> ?

5 seconds -> ?

Remember the goat in the 40 foot square pen?

The goat is on a 40 foot rope, tethered
to one of the corners. There a square obstruction
in the middle of the grassed 40 x 40 pen.

Each side of the obstruction is 16.5 feet from
the nearest fence line. Neither the goat nor the rope
can pass thru the obstruction.

How many square feet can the goat graze.

(Figure to the nearest 1/100 of a sq ft)

Grid Probability

The grid image below is not drawn to scale ... consider a grid like the one pictured, in which each space is a perfect square. If you toss a coin ( either penny, nickel, dime or quarter... the coin should be smaller than a square ) randomly onto the grid, what is the probability of the coin landing on a corner of one of the squares?

Space Message

After all these years, it has finally happened. We have received an intelligent message from somewhere in space. Nasa and Seti are so excited ... but what does it mean?

Can you help decipher the message?

Prove that...

ok, here are some proving questions:

1) if H is the set to infinity of all positive integers, none of which have prime factors greater than 3, the PROVE THAT: the sum of the reciprocals of elements of H are smaller than 3

2) PROVE THAT any prime number (2^(2^n) + 1) cannot be represented as a difference of 2 fifth powers of integers.

NOTE: just for confirmation, this 2^2^n is the same like my last question, it is a continuation of it that i just found.

3) a₁ , a₂ , a₃ , ..... , a2009 are real numbers.

a₁ + a₂ + a₃ + ..... + a2009 >= 2009²

and, a₁² + a₂² + a₃² + ..... + a2009² <= 2009³ + 1

then, PROVE THAT 2008 <= a k <= 2010 for all values of k belonging to the set (1,2,3,4,.....,2009)

NOTE: here k is a subscript

Guess the Picture

Here is the next drawing puzzle, Guess the picture !

Assorted questions

OK, these are just some assorted questions that I have, rather than putting many posts, I am putting them all in one as they aren't very difficult, but please post HOW you did it, I want more methods to solve them :)

1) p(x) is an expression. and it satisfies, 2p(x) + p(1/x) = x+1. find p(2)

2) Find the Sum of digits, and number of digits, of the number: (1000^20) -20

3) Find the last integer of the number (((2)^2)^n) + 1 and prove it. only for n>1(not using trials :P )

4) x = (-1 (+/-) rt(-3))/2 find the value of (x^1999 + x^2000) = ?

5)a+b+c = 0 ; (b^2 + a^2 + c^2) / (b^2 - ac) = ?

All of these are 10th grade problems, so should be easy.

Senior class

It appears that an ingenious or eccentric teacher being desirous of bringing together a number of older pupils into a class he was forming, offered to give a prize each day to the side of boys or girls whose combined ages would prove to be the greatest. Well, on the first day there was only one boy and one girl in attendance, and, as the boy's age was just twice that of the girl's, the first day's prize went to the boy. The next day the girl brought her sister to school, and it was found that their combined ages were just twice that of the boy, so the two girls divided the prize. When school opened the next day, however, the boy had recruited one of his brothers, and it was found that the combined ages of the two boys were exactly twice as much as the ages of the two girls, so the boys carried off the honors of that day and divided the prizes between them. The battle waxed warm and on the fourth day the two girls appeared accompanied by their elder sister; so it was then the combined ages of the three girls against the two boys, and the girls won off course, once more bringing their ages up to just twice that of the boys'. The struggle went on until the class was filled up, but as our problem does not need to go further than this point, to tell the age of that first boy, provided that the last young lady joined the class on her twenty-first birthday. What is the first boy's age (at the start).

3 Feb 2010, 6:10 AM. Express your answer in days.

Badly made wagons

When they started off on the great annual picnic every wagon in town was pressed into service. Half way to the picnic ground ten wagons broke down, so it was necessary for each of the remaining wagons to carry one more person. When they started for home it was discovered that fifteen more wagons were out of commission, so on the return trip there were three persons more in each wagon than when they started out in the morning. Now who can tell how many people attended the great annual picnic?


I should have called this one "Buggy wagons" - too late.

A Week Apart

Christmas and New Year's Day are exactly one week apart, so they always fall on the same day ... or do they?


Can you think of a year in which they would fall on different days?

The Earlier Birthday

Twins were born ... obviously one before the other. The second born now celebrates his birthday a day earlier than his older brother.


Why?

The Arrest

A man enterred a gun store and began to request unusual quantities of ammunition. The store owner was suspicious and told the man he would have to go into his storeroom to get the large order. While in the storeroom, the owner called the police.

The police arrived and questioned the suspect as to why he needed such large quatities of ammunition. The man explained that he was having a target shooting competition and pulled the following flyer from his pocket:

------------ YOU ARE INVITED ------------
--- TARGET SHOOTING COMPETITION --
----- DRINKS --- BUFFET --- DINNER ----

Where? -----Straight Shooter Hunting Lodge
When? ----------------- Saturday, August 10
Who's invited? ------------- All Your Friends

Wiley Jane Ted Tom Art Corky Kate Ray Myron
Tracy Grady Trudy Hank Wes Norm Flo Dan
Andy Sandy

The sharp-eyed policeman looked closely at the flyer for several minutes. He then told the suspect he would have come to the station for more questioning.


What was it about the flyer which gave the officer concern?

One Doesn't Belong

One of the following does not belong with the others:

beginning
plummet
curtail
modesty
tapestries
prosecute
hatred
finagle
chartreuse


Which one? ... and why?

4-Digit Number

Can you find a 4 digit number with these properties?:

the first digit is 1/3 of the second (the 1st digit means from the left side)

the third digit is the sum of the first and second

and

the fourth is 3 times the second


What is the number?

No Electricity

A bad storm knocked down trees, which fell across power lines, and put a small town in the predicament of having no power. Although highly unusual, both of John's headlamps on his truck had burned out recently. As John drove carefully, he nearly hit a blind man who was crossing the street.

With no headlamps, and no street lights, how was John able to see the blind man in time to avoid running him over?

Lowest Number

If you divide a particular number by 4, there's a remainder of 1; if you divide the same number by 5, there's a remiander of 2; and if you divide it by 6, there's a remainder of 3. There's probably lots of numbers which would meet the stated criteria.

What is the lowest number which complies with problem statement?

How Cold?

With great reservation, in anticipation, of an onslaught of crazy, wild speculation, tempered with some intelligent questions, I pose the following:

(Look out, take cover, duck, and any other means by which to protect yourself ... heh heh!)

In your opinion, what temperature, in Farenheit, would be twice as cold as 0 degrees Farenheit?

TOM'S Golf Course

TOM's new golf course is a nine hole course. Yardages for the individual holes are as follows:

Hole 1 - 300 yds.
Hole 2 - 325 yds.
Hole 3 - 225 yds.
Hole 4 - 250 yds.
Hole 5 - 275 yds.
Hole 6 - 400 yds.
Hole 7 - 200 yds.
Hole 8 - 350 yds.
Hole 9 - 375 yds.

Karl, the course Pro, has received a new set of experimental clubs. Each club mysteriously hits the ball the same distance everytime (within a foot or two). The new clubs also never produce a slice or hook. The club distances are as follows:

1 Iron - 250 yds.
2 Iron - 225 yds.
3 Iron - 200 yds.
4 Iron - 175 yds.
5 Iron - 150 yds.
6 Iron - 125 yds.
7 Iron - 100 yds.
8 Iron - 75 yds.
9 Iron - 50 yds.
The new putter will sink any putt within a few feet of the hole.

Karl always uses a caddy to carry his bag. However, today, his ususal caddy, Knightmare, is asleep on his couch and did not arrive. Karl decides to play the course anyway and to avoid carrying the heavy bag, will play with just two irons and the putter.

If he choses the 8-iron, the 6-iron and the putter, he figures he can complete the round in 37 strokes (28 approach shots and 9 putts). If he overshoots a green, back shots are acceptable.

He really wishes Knightmare was here to help him decide which 2 clubs would give the best score.

If you were caddying for Karl, what 2 clubs (and the putter) would you recommend to beat a round of 37?

The Goat Eats

There is a fenced in area of grass which is 40' x 40'. There is a vertical metal pole mounted securely, in the ground, in the center of the fenced in area. A goat is placed inside the fence with a 20' rope tied to the collar around its neck.

How much grass can the goat eat?

Eight Dogs

A man has eight dogs ... 4 brown, 3 white, and 1 black. How many can say they are the same color as another dog?

The Next One

The words in the following list follow a pattern:

longer
teamwork
therefore
flour
effusive


Can you find the pattern? ... and once you do, how many words can you add?

In Common

The following list of words have something in common:

heart - known - travel - apathy - closest - irate - loner - amulet - hired - factory - acronym - against - sandy - filly - magenta


What's their commonality?

(Chris + Zaux ) / Wiz = IXX.RZAZ

Here's a unique puzzle.

I have never seen one of these with a divide.

(Chris + Zaux) / Wiz = IXX.RZAZ

Each letter in the equation above represents a
different digit. Can you crack the code?

Add the first two (Chris + Zaux)
Then divide by the third. Wiz
The result is rounded to 4 decimals.
Note the decimal between IXX and RZAZ

Photo Emotions

Can you find 5 simple emotions hidden in these rectangles

Five and Two

To express the number 25 using only one 5 and one 2, you could write -> 5^2 (this site wouldn't allow posting of a superscript ... however, if you were writing you could express 25 with only a 5 and a 2).

Can you find another way to express 25 using only one 5 and one 2 and two arithmetic operators?

Pizza Anyone?

A club of 30 members ordered pizza. One of the members commented that it 5 people had not attended, the price per person would have been $2 more.

What was the total bill for pizza?

Share the Profits

A small restaurant business ended its year with $7920 in a profit sharing plan for its employees. The cooks profit sharing amounted to $302 more than the waitress, $882 more than the busboy, and $960 more than the dishwasher.

How much did each receive?

How Much Fabric?

Six types of fabric were discontinued at a store. The fabric left on each roll was:

30 meters
32 meters
36 meters
38 meters
40 meters
62 meters

The discontinued fabric was put on sale at half price. Two rolls sold the first day. On the second day of the sale, 3 more sold. The total length of fabric on the 3 rolls sold the second day, was twice the total length of the 2 rolls sold the first day.

One roll of half price fabric remained ....

How much fabric was on the last roll?

100 Chickens

A farm hand was sent by his employer to buy chickens. He was given $100, and told, to purchase 100 chickens. He bought a $2 hamburger, and was still able purchase 100 chickens.

Pricing:

Hens ----- $5
Roosters - $2
Chicks ----$1 for 2

When he returned to his employer, he had no money and 100 chickens.


How many of each did he purchase?

Catch the Football

A father and his son are tossing a football. Each time the father receives the ball, he throws it and then steps back 3 feet. When the total distance the ball has been thrown reaches 195 feet, the boy fails to catch the ball.

(amendment: the Dad throws first)

How many times is the ball thrown?

What is the distance of the last throw?

The Hunting Dog

Two brothers go hunting separately, but in the same area. Having only one dog, they toss a coin to see which one the dog accompanies. After a while, both are on higher ground a half mile apart, and they spot each other. They begin to walk toward each other at 2.5 mph. The dog also spots the other brother and runs ahead to meet him, at 9 mph. The dog runs back and forth between the two brothers until they meet.

How far does the dog run?

How Big It Is?

Multiply 2 x 2 one hundred times ...

What is the answer?

Countries of Latitude

If a plane leaves London, England and flies around the globe at 51 latitude, it will fly over 9 countries.

Name the nine countries.

The Next Letter

This is a tough one.

What is the next letter?:

M -- V -- E -- M -- J -- S -- U --