What They had in Common

Besides tyranny and a thirst for world domination, these 6 leaders had something else in common:

Hitler
Mussolini
Napoleon
Genghis Kahn
Julius Caesar
Alexander the Great


What did they have in common?

It's What?

It's invisible.
It doesn't smell
Passes through solid objects.

What is it?

What is the Landmark?

The distances from several cities to a famous landmark have been measured. The distances are close enough in accuracy to determine the landmark:

1,124,640 ft. ------- London

39,330,720 ft. ------ Honolulu

4,414,080 ft. ------- Oslo

23,400,960 ft. ------ Fairbanks

10,565,280 ft. ------ Cairo

31,954,560 ft. ------ Tokyo


What is the landmark, and where is it located?

Simple Things

Name 3 things, that everything in the universe, is continuously doing!

(every thing includes animate and inanimate)

Simple Maths

Baileyville, IL – Dolton, IL = 588 = Blackfoot, ID – ?

- Matt Stephans

It's How Old?

There are really old things. There are some very old living things.

What is the oldest living thing? (on planet Earth)

A Double Century

When will the beginning of a century fall on a Sunday? (Note to pedants: for this question, I define the centuries as beginning with the year ending in 00, not 01.)



To help you in your quest…



There are no agreed-upon leap year rules with timescales longer than 400 years, so what we have is one fixed pattern that repeats itself exactly every 400 years. No, I'm not telling you what the pattern is.... look it up on wikipedia at your peril!



Now keep in mind that a fair amount of tinkering with the calendar occurs now and again. Our current (Modern Gregorian) calendar was instituted on Friday, 15 October 1582, and took a couple hundred years to be generally adopted. Prior to this, the year 1100 had started on a Sunday, but timekeeping was so generally screwed up back then that when the Gregorian system was adopted, a bunch of days had to be removed to get the dates to synch up correctly with the seasons. (In the U.S., the missing days were September 3 through 13, 1752.)



Next question…There is already talk (premature in my opinion) that to get the current calendar to remain accurate, we'll need to eliminate one extra leap day every 4,000 years. Bearing this in mind, and the extra leap day is eliminated, when will the beginning of a Century then fall on a Sunday?

- Karl Sharman

Number LOGIC

This is not my problem. If it had been mine, I would have included the exponent of three as a letter.


Decode the letters into the proper digits.


The individual numbers of LOGIC are added, that sum is then cubed. The result has the
same as the digits that you began with.


(L+O+G+I+C)^3= LOGIC


Note that only five different digits are used.

Couch Theft

Someone has stolen Knightmare's couch! Detectives Zaux, Karl, Cam, Wiz, Ragknot, and Cam immediately locate 4 suspects. When questioned by the police, they each make a statement:

A. I was not in town at the time of the theft

B. C is the culprit

C. B's statement is false

D. C's statement is true

Everyone is telling the truth except the guilty one.

WHO STOLE KNIGHTMARE'S COUCH?

UNKNOWNS

[3(230+t)]^2 = 492,a04

t = ?

a = ?

Rain or Shine?

In London, it it raining at midnight ... will the weather be sunny in 72 hours?

Bicycling and Walking

Two friends decide to take a bicycle trip. During their journey, one of the bikes malfunctions and has to be left behind. The friends decide to continue their trip and share the remaining bicycle. They start again, one riding and one walking. At some point, the rider gets off the bike, leaves it and continues on foot. When the boy, whose bicycle failed, reaches the abandoned bicycle, he gets on and rides until he catches up with his buddy, who then takes the bike again. This plan continues until they reach their destination.

The distance from the point, where the bicycle malfunctioned, to the destination is 60 miles. When walking, each walks at 5 miles per hour, and when riding, each rides at 15 miles per hour.

How far from the destination should the last boy to ride, abandon the bike so that he and his buddy reach the destination simultaneously?
(amendment: neither boy is wearing a watch)

English Comprehension Test

(especially for Chris ... and the rest of you puzzlers)

My age, which plus yours is 86, is 15/16 the age you will be when I am 9/16 the age you would be if you were twice as old as I will be when I am twice your age.

How old are we?

(I fear we will be much older when we comprehend this problem statement)

What time Is It?

Two watches show the same time. One of them is 1 second fast per hour. The other is 1 1/2 seconds slow per hour.

When will they show the same time again?

When will they show the correct time again?
(amendment: both watches)

Small and Large Numbers

If you have 2 numbers, and you subtract half of the smaller number from each number, the result from the larger number is 3 times the result from the smaller number.

By how many times is the larger number, larger than the smaller number?

or

You have 2 numbers.
One of the the numbers is bigger than the other one.
Find out what one half of the smaller number is.
Subtract the one half amount from both of the 2 numbers.
After you subtract, you will have 2 new numbers... the new larger number is 3 times as big as the new smaller number.
Is the original larger number 1, 2 , 3, 4, 5, 6, etc. times larger than the original smaller number?

Escape from the Vampire's Castle

Three travelers, in a horse drawn wagon, were heading to the nearest village to purchase medicine for a family member, who was gravely ill. Because the distance to the village was a three day ride, they decided to travel day and night, taking turns at the horse reins.

During the second night of travel, they were attacked by a vampire. He captured them, tied them up, and using their wagon, took them back to his castle. His captives were taken up a circular staircase and placed in the small room at the top. He freed their bonds, and locked the door as he left.

The plain circular room has one window. Looking for an escape, Rendal looks out the window and sees something which may assist them. This tower of the castle must have been recently added, because the masons left a 2 bucket, rope, and pulley system attached to the top of the tower. The buckets had been used to raise stone and lower debris during construction. A sign on one bucket indicated that the bucket weight differential should be 10 lbs. This weight differential would allow the heavier bucket to slowly descend to the ground while raising the other to the window. Stacked against the wall, Rendal noticed 13 roughly hewn stones, each weighing very close to 10 lbs. They had obviously been used by the masons as counterweights for the bucket system. The buckets seemed large enough to carry a person.

Rendal weighed 180 lbs. His wife, a small lady, was 100 lbs, and their young son tipped the scales at 80lbs.

As the sun rose the next morning, the vampire slept. Rendal and his family used the bucket system to escape the tower. They found their wagon and hurried away from the castle to purchase the needed medicine.

(amendment: the 13 roughly hewn stones were stacked against the wall in the room in which the people were held captive)

Explain how they accomplished the escape.

Knightmare Runs

As Knightmare stretches for his afternoon run, he notices 12 signs along the trail. There is an equal distance between each sign. He begins waddling ... oops ... I meant he begins running and reaches the 8th sign in 8 seconds.

Altogether, how many seconds have elapsed when he reaches the 12th sign?

Growing by Denominators

Find the smallest fraction, which will triple in size, when you add its denominator to its numerator and its denominator.

Find the smallest fraction which will quadruple when the same process is applied.

Time for a New Watch

In an environment with extreme temperature fluxuations, a scientist noticed his watch was 1/2 minute fast at nightfall, but at dawn, it had lost 1/3 minute, making it only 1/6 minute fast. On the morning of May 1, he accurately reset his watch.

On what date was the watch 5 minutes fast?

(an easy one)

Timely Deliveries

A delivery driver is suppose to arrive at his destination at exactly 11:00 AM. If the truck travels at 30 mph, it will reach the intended delivery point at 10:00 AM, an hour early. If the truck travels at 20 mph, it will arrive at noon, an hour late.

How many miles is it to the destination? ... and how fast should truck travel to make delivery on time?

Chris, Zaux, Wiz = Arias

Chris + Zaux + Wiz = Arias

Each letter in the sum above represents a different digit.

Can you crack the code?

There's one solution to this one.

How Much Farther?

Two friends were 59 miles apart before Karl started. Karl travels 7 miles every 2 hours. Ragknot travels 8 miles every 3 hours. Ragknot started an hour later than Karl.

How many MORE miles will Karl travel before he and Ragknot meet?

(amendment: --> they are traveling in a straight line towards each other)

Free gifts

A breakfast cereal includes a free gift is included in each box. There are six different gifts. Assuming there is an equal chance of getting any one of the gifts, what is the expected number of boxes you need to buy in order to get all six gifts?

Average number

If the probability of an event happening in one trial is p, the average number of trials needed to get the event is 1/p. Why is that true?

Loan Me Money for a Guitar

Three bothers buy a guitar for $100 (jeez! I hate they wasted their money on such a cheap instrument ... but anyway). The youngest brother said he could have purchased the guitar by himself, if the middle aged brother had given him half his money. The middle aged brother said he could have purchased it by himself, if the oldest brother had given him a third of his money.
The eldest brother, checked his funds, and added, he could have purchased the instrument himself if the yougest brother had given one fourth his money.

How much did each brother have prior to the purchase of the guitar?

(there's not a published solution, but I solved it to verify answers)

(and do you know a pawn shop where they might have found a better instrument... these guys are never going to learn to play with a crappy guitar ... the action is too high ... the cheap machines don't hold precise string tension ... oh wait ... sorry .... has nothing to do with this problem... heh heh)

Three to Gamble

A game of chance and some skill ensues between 3 professional gamblers. In the first game, gambler A loses to gambler B and C an amount of money equaling the amount each possessed before the game. In game 2, gambler B loses, to gamblers A and C, an amount of money equaling the amount each had before game 2. In the 3rd game, gamblers A and B gain from gambler C as much money as they had before game 3. After game 3, each man checks his money and each has $24.

How much money did each gambler have before the first game?

(for this one, I have no solution ... so, I am counting on you guys to cuss, discuss and sort it out... and for those purists in the crowd, "cuss" is informal for "curse" ... heh heh)

Rabbit on the Run

A dog spots a rabbit which has a 150 ft. head start, and gives chase. Each jump of the rabbit covers 7 ft. and each leap of the dog covers 9 ft.

How many leaps must the dog make to catch the rabbit?

Lots of answers

This will be interesting. If you have found these difficult, this
may make it easier to find a solution.

Trick + Of - Mind = TONIC

Each letter in the equation above represents a different digit.
(Ignore upper / lower case)
Hint: There are 484 different solutions!
Also the first code of any "word" will
not be zero. Can you crack the code?

Please give the solution(s) using a
string of digits that correspond to the key.


TRICKOFMND <-- ten letters I call the KEY..

xxxxxxxxxx <-- ten digits, called "My String" .

that correspond to your solution to the key..

Example > "7234561890" .

(BTW that's not one of the answers.)
In this case you be setting T=7, R=2, etc.

Gambling with Dice

Two gamblers decide upon a game of dice with the following rules:

Gambler Albert (A) wins if he rolls 6 before Gambler B rolls 7.

Gambler Edward (E) wins if he rolls 7 before Gambler A rolls 6.

A coin toss has determined that gambler Albert will roll first ...


Which gambler has the better chance of winning? ... and why?

Horses and a Will

Seventeen horses are to be divided among three sons, according to a man's will. The will states the oldest son gets 1/2 of the horses, the middle aged son gets 1/3, and the youngest gets 1/9. An obvious solution involves horse meat for dinner ... but the sons agree they do not want to harm their father's horses.

How did they divide the horses and still comply with the stipulations in the will?

A Bee in the Hand

If there's a bee in your hand, then what is in your eye?

Squared Sets

In a set containing 3 numbers, each is squared, the squares are added, and the total is 139.

In another set containing 6 numbers, each is squared, and added for a total of 139.

(a number may appear in both sets)


Identify and list both number sets.

Knightmare Running

Knightmare (one of our fellow puzzlers) has decided to improve his fitness by jogging ... heh heh.
He stands from the couch, dons running gear, and hits the road. Upon approaching a long, familiar railroad bridge, he knows it will take 3 minutes for him to cross. He is 1/4 of the way across when he hears the train whistle behind him. Being familiar with the road, he knows the crossing where the train just whistled, and he knows the speed of the train. He calculates it will take 1 minute for the train to reach the bridge. If he continues forward, he realizes he would be 15 seconds from the end of the bridge when the train stikes him. He also calculates that by turning around and heading back, he will have just enough time to exit the bridge before the train reaches it. His jogging speed is 8 mph ...

What is the speed of the train?

The Sculpture Support

An artist has been commissioned to do a sculpture which will sit in front of the post office in the small community of Puzzleville. The artist decided to pour a cement footing and place a verticle pipe in the cement to stabilize his art. One third of the total length of the pipe was placed in the ground. He decided to paint the above ground section to prevent rust. With his step ladder, he could only reach and paint 1/2 of the total length of the pipe, leaving 4 ft. at the top unpainted.

What was the total length of the pipe?

Hmmm ... what is it?

Things it's not:

liquid
gas
solid
animal
plant
mineral

Things it is:

transparent, but visible
always in motion
man's best friend or worst enemy

Additional hint:

it has no gender, but reproduces itself

What is it?

Alien Shrinkage

Our life-giving sun is approximately 800,000 miles in diameter. Suppose an alien space vehicle invaded our solar system, and using technology far beyond our comprehension, somehow reduced our sun to a diameter of 9 ft. And then, being amused at their accomplishment, they reduced the rest of our solar system proportionately.

Based upon the reduction is sun size, how would you estimate the following sizes and distances?:

a. Earth's diameter (inches)

b. Mars diameter (inches)

c. the distance from Earth to Mars (feet)

d. the distance from Earth to the Moon (inches)

e. the distance from our Sun to the nearest star, Proxima Centauri (miles ... which are also reduced proportionately)

Ball breaking

Your job is to determine the highest floor of a 100 floor building from which a snooker ball may be dropped without breaking. You have two identical snooker balls. If a ball doesn't break, it is completely unharmed. If both balls break before you have determined the highest floor, or you drop the balls more times than is necessary, then you'll need to to seek alternative employment. What is the maximum number of times you have to drop the balls?

For consistency, assume the floors are numbered 1 to 100 in your explanations. Also assume, that there is no need to drop a ball from floor 1 (the ground floor).

Trick of Mind >>> be informed

Ok the title is not exactly this puzzle. I found out it is not easy to make up a puzzle like this that makes sense. I want to say something like GREAT, but that didn't work out.

TRICK + OF + MIND = INFORM

Each letter in the sum above represents a different digit.

Hint: There are two different solutions
K and D can swap value, and the equation remains true.
Also the first code of a "word" will not be zero.
Can you crack the code?

Three card trick

On your travels you come to an old man on the side of the road holding three cards from a standard deck face down. Trying to make conversation you ask him what the three cards are. He tells you, "To the left of a queen, are one or two jacks. To the right of a jack, are one or two jacks. To the right of a club, are one or two diamonds. To the left of a diamond, are one or two diamonds". What are the three cards?

Use your skills to interpret the above to arrive at a unique answer.
I rate this one as easy. I'm only posting it to give Zaux a break.

Getting Dressed

Three friends were getting dressed for a Puzzle Convention.

1. Chris did not wear leather

2. The person in cotton was wearing either yellow or blue

3. The person in blue wore either leather or wool

4. The person in cotton was Knightmare or Ragknot

5. Chris was not in blue

6. Ragknot was in red or blue


What did they wear?

Four of a kind

With four decks of cards, what is the minimum number of cards that you must draw to get four of a kind?

---
25 Jan 2010 5:10PM
Sorry people, I should have gone to bed instead of posting. The question should have been:

With four decks of cards, what is the minimum number of cards you must draw to be assured of getting four of the same value, ignoring the suite?

Angular Velocity

Just above a merry-go-round, a 35-kg child rests on a low hanging tree limb. The merry-go-round is a solid disk of radius 2.0 m and a mass of 160 kg. It is spinning at 3.0 rpms. The child gently drops onto the merry-go-round at a point 1.0 m from the center.

Spinning together, what is the new angular velocity?


(okay ... Knightmare talked me into it ... maybe one good puzzle a day ... and a genuine thanks to everyone who expressed appreciation for my puzzle posting efforts)

The Same Birthday

Although their ages are different, three children share the same birthday. On the last birthday, one of their ages was the sum of the other two. A few years later on their birthday, the youngest noticed that one of their ages was half the age of the other two added together. Since the birthday, on which one age was the sum of the other two, the number of years which had passed was half the sum of all the ages on the birthday when one age was the sum of the other two ... one was celebrating an 18th birthday ... which birthday were the other two celebrating?

(this is a test of Chris's english comprehension skills ... heh heh)

The Mailing

A mail room employee of a business was asked to send a mailing to a 10% sample of their customers. Rather than randomly selecting the customers, he devised a selection scheme. He picked the first name on the list, skipped one and picked the next one, skipped two and picked the next, and so forth until he came to the end of the list. To his surprise, the last name selected was the last name on the list. Also, upon examination, he found that his system had selected exactly 10% of the names on the customer listing.

How many names were on the mailing list?

The Army Advances

An army 4 miles long advances steadily for 4 miles along a straight road. A dispatch rider leaves from the extreme rear and rides to the front to deliver important information to the commanding general. Although different speeds, the army's and the rider's speed remain constant. After delivering the info, the rider gallops back to the rear.

How far has the rider traveled?

Lettered Equations

In the following lettered equation, each letter represents a digit:

TIM x SOLE = AMOUNT

Using the same substitution code, the difference between LEAST and MOST is ALL. Please understand, I did "not" say LEAST - MOST = ALL, but rather that the difference between the two equals ALL.

Break the code and write both equations with numbers!

Mystery Number

Can you determine the missing number in the following sequence?:

9 --- 22 --- 24 --- 12 --- ? --- 13

4 Digits and a Square

Target: 4 digit number

Criteria:

1. add the number formed by the first 2 digits to the number formed by the second 2 digits

2. the square of the results of step 1 equals the original 4 digit number

3. there is another number, with a 1000 difference, from the original number, which also complies with criteria in steps 1. and 2.

Flight of the Rocket

A rockets launch site is 2000 ft. from the control center. The rocket blasts off vertically at the rate of 500 ft./sec. After 10 seconds, how fast is the distance changing between the rocket and the control center?

Complete the Words

Fill in the missing letters with a 2 word phrase which completes a 4 letter word in each column:
(you will place one word of the 2 word phrase in row 1, and the second word in row 4)

---- ? ---- ? ----- ? ---- ? ---- ? ---- ?

---- S ---- E ---- O --- A ---- L --- O

---- E ---- A ---- T --- C ---- S --- E

---- ? ----- ? ---- ? ---- ? ---- ? ---- ?

A 10-digit Number

Can you find a 10-digit number such that:

1. it has m digits between the m's, n digits between the n's, and so forth

2. its first digit is a prime number

3. the 2 digit number formed by its 2nd and 3rd digit is also a prime

4. the 3 digit number formed by its 4th, 5th, and 6th digits is 3 times a prime

5. and the 4 digit number formed by its last 4 digits is also a prime

Find the number.

What's the Word?

As you can see, the following groupings of letters are the central letters in words. Each grouping begins with two letters and ends with the same two letters in the same order. (For clarification, the two letters are different for each grouping.)

1. **ca**

2. **bl**

3. **eepi**

4. **adac**

5. **ur**

6. **gib**

7. **risco**

8. **epsa**

I'm not sure if there is more than one answer for each, but I have at least one for each.

Can you find the words?

What Does It Mean?

The following each represent a different word or phrase, and they have a common theme.

1. + am

2. jojojof

3. $a$r$d$

4. in ... not out

What are the 4 words or phrases, and what is the common theme?

Selling Books

200,000 is the quantity of a particular book which a publisher plans to sell in a year. It costs $3750 to set up the printing. The actual printing of each book costs $3. And to store 1000 books for a year cost $600.

What size printing runs will minimize the publisher's cost?

Rectangle and Parabola

Find the dimensions of a rectangle of maximum area, whose base lies on the x axis, and whose upper vertices lie on the parabola y = 12 - x^2. And what is the maximum area?

Square in a Triangle

Consider an equilateral triangle with sides of length 20. Find the area of the largest rectangle that can be inscribed in the triangle.

Cylinder in a Sphere

What is the largest possible volume a right circular cylinder can have if it is inscribed in a sphere of radius 5?

How Close the Ships

Ship B is 100 miles east of ship A at noon. If ship B sails west at 10 mph and ship A sails south at 20 mph, at what time will the ships be closest to each other? At that time, what is the distance between the ships?

Growth of an Angle

5 and 10 inches are 2 sides of a triangle. The angle between them is increasing at the rate of
5 degrees per minute. How fast is the third side of the triangle growing when the angle is 60 degrees?

(I have an answer, but no detailed solution)

Toll Road Profit

A toll road in Puzzletown averages 300,000 cars a day when the toll is $2.00 per car. A detailed study has proven that for every $.10 increase in the toll, 10,000 fewer cars will use the road each day.

What toll maximized the revenue?

The Pirate's Treasure

The pirate, One-eyed Pete, hid his treasure on an island. The island was divided into a 4 x 4 grid of equal sized squares. Each square was assigned a color. He wrote the following info on his map:

1. The blue square was one square horizontally to the left of the pink square.
2. Orange was one to the right of and one above the white.
3. The red was one square vertically above the purple.
4. Lavender was one square horizontally to the left of indigo.
5. The brown was one vertically below green.
6. The purple was one horizontally to the left of the gray.
7. Violet was two horizontally to the right of yellow.
8. The indigo was one vertically above the white.
9. Turquoise was two below and one to the right of the red.
10. The crimson was one to the right of and one below the green.
11. The GOLD square was where the TREASURE was buried.

Describe the location of the treasure on the 4 x 4 grid.

Mixed Up Titles

This information is the titles of the first four place winners in the Unusual Book Title Competition. The titles got mixed up and only one word in each column is in the correct position.

PLACE -- 1st WORD ----- 2nd WORD ----- 3rd WORD ----- 4th WORD

-- 1 ------- Killing ---------- Puddings -------- Laughing ------- Stupidly

-- 2 ------ Making --------- Sharks ----------- Jumping -------- Loudly

-- 3 ------ Hitting ---------- Cakes ------------ Running -------- Cruelly

-- 4 ------ Shooting ------- Flies -------------- Hopping -------- Quickly


The following will help you arrange the words in the book titles correctly:

1. Jumping is not adjacent to Running

2. Sharks is one place below Loudly

3. Killing is one place above Quickly

4. Sharks is not in the same title as Running

5. Making is one place below Jumping.

6. Cakes is one place above Running


Correctly sort the words in each unusal book title and it's place in the competition.

Bag of Balls

A bag contains 9 colored balls: 3 red, 3 yellow, and 3 green. Three balls are removed from the bag, one at a time.

1. The first and third ball removed were not a pair of yellow and green.

2. A green ball was removed before a red one, if and only if, a yellow was taken after a red.

3. A green was not removed later than a red one.

4. The first color removed was different from both the second and third.

What color were the 3 balls removed from the bag ... and in what order were they taken?

Witches Brew

Double, double toil and trouble,
Fire burn and cauldron bubble.

A witch was brewing a concoction for a spell. In her cauldron, she placed the following ingredients:

dishwater
castor oil
dirty snow
crushed pig's ear
sheep droppings

The dishwater was one half the cauldron volume; the castor oil one third; dirty snow was one quarter; crushed pig's ear was one fifth; and sheep droppings were one sixth.

The total volume of the second and third ingredients added was less than half of the cauldron volume. Castor oil was added later than the crushed pig's ear, but earlier than the dishwater. Dirty snow was added two places after the sheep droppings. Oops! the cauldron spilled over.

In what order were the ingredients added?

100

Using only 16, 17, 23, 24, 39 and 40 and addition, make 100 with the minimum number of numbers. e.g. 40+39+21=100 uses only 3 numbers - unfortunately 21 isn't available. You may use a number more than once e.g. 23+23+... is ok. What are the numbers?

Doubling up

Five schoolchildren were weighed in pairs. Their (combined) weights were:
129, 125, 124, 123, 122,121, 120, 118, 116 and 114 lbs. What were their individual weights?

When the wind blows

A cyclist cycled a mile in 4 minutes against the wind. He returned in 3 minutes. How long would it have taken if there was no wind?

Merry-Go-Round

Whilst riding on a Merry-Go-Round, ToM noticed that the total number of riders was equal to one-third of those ahead of him plus three-quarters of those behind him. How many riders were there?

For the birds

There are two trees with birds in them. The birds in one tree say to the others, if one of you joined us, we'd be twice as many as you. The birds in the other tree say, if one of you came over here, then we'd have just as many as you.

How many birds are in each tree?

Hat colour

Three men A, B and C are captured by cannibals. They are tied to stakes. A can see B and C. B can only see C. C can't see either A or B. They are then shown five hats. Three are black and two are white. The men are then blindfolded. A hat is put on each one's head, the remaining two hats are hidden away and then the blindfolds are removed. They are told that if one of them can call out the colour of his own hat, they can all go free. Otherwise they'll really be in hot water.

After a short time A calls out, "I don't know my hat colour". Soon B calls out, "I don't know my hat colour either". C thens called out the colour of his hat.

What colour is C's hat?

Divisible by 3?

As I haven't seen it be posted before: prove that if an integer is divisible by 3, that the sum of it's digits are as well.

Also show that the remainder after division by 3 of the sum of the digits is the same as the remainder after division by 3 of the original integer.

Three bags of marbles

You have three bags of marbles. The first bag contains two white marbles, the second contains two black marbles and the third contains one black and one white marble.

You pick a bag at random and take out a marble. It is white. What is the probability that the remaining marble in that bag is white?

Minutes 'til Six O'clock

50 minutes ago, the number of minutes past 3 o'clock, was 4 times the number of minutes, that is it now 'til 6 o'clock.

How many minutes is it 'til 6 o'clock?

What's the Next One?

Look at this series:

1 -- 6 -- 2 -- 7 -- 3 -- 8 --

What are the next 6 numbers in the series?

How Far?

You are a professional sign maker. The local government issues a requisition for you to paint a sign. The information to be displayed on the sign was given to you:

PUZZLETOWN -- 15 MILES

CONFUSEDVILLE -- 25 MILES

VILLAGE OF ILLOGICAL THOUGHT -- 50 MILES

At the last moment, you receive a phone call requesting you to add one more name:

TOWNSHIP OF MISCONSTRUED

You ask the caller how many miles ... she said just use the same logic as for the other names.

You look at the names and say "OK".

How many miles to the TOWNSHIP OF MISCONSTRUED?

One More Race

Chris, Cam, Antn'y, Karl, and Zaux decide to have a foot race. Chris, feeling a little guilty about the case of booze he lifted from the tavern, decided that it should go to the winner. Knightmare drove his supercharged couch to the track and while resting comfortably, volunteered to be the official race starter.

Knightmare lowered the flag and the 3 mile run officially began. Knightmare wiped perspiration as the runners completed lap after lap ... in fact, he got so tired, he fell asleep and did not witness the finish.

Since Knightmare also had the obligation to present the winner with the case of booze, he panicked and asked a young kid playing nearby if he had watched the race. The young boy replied:

* There were no ties
* Chris did not come in first
* Cam was neither first nor last
* Antn'y came in one place after Chris
* Karl was not second
* Zaux was two places below Karl

Knightmare thanked the boy, and presented the booze to the winner.

In what place did each racer finish?

Lets count the fingers again

Lets count the fingers again, but
a little different. Use both hands,
Start with one as the little finger of the
left hand. Count left to right so the left thumb is 5.

Continue with the right hand. But lets suppose the right
thumb is missing. 6 is the right index finger, and 9 is
the right little finger.

Don't recount the little finger so 10 is the right
ring finger.

Just keep counting all nine fingers left to right then
right to left. Which finger is # 123456789 ?

Need help? lets count to 17

Left Little" '1
Left Ring" '2
Left Middle" '3
Left Index" '4
Left Thumb" '5
Right Index" '6
Right Middle" '7
Right Ring" '8
Right Little" '9
Right Ring" '10
Right Middle" '11
Right Index" '12
Left Thumb" '13
Left Index" '14
Left Middle" '15
Left Ring" '16
Left Little" '17

The Truth

One, and only one, of these statement is true:

A) One of these statements is FALSE

B) Two of these statements are FALSE

C) Three of these statements are FALSE


Which one is TRUE?

Finger counting

Start counting on the fingers on one hand thusly: 1 thumb, 2 index finger, 3 middle finger, 4 ring finger, 5 little finger, 6 ring finger, 7middle finger, 8 index finger, 9 thumb and so on.

Which finger would you end up on if you were counting to 123456789? That over 123 million in case you think it's a trick question. Assume that you aren't carted of to the funny farm while doing it.

The surprise prize

You have a friend who is a logician (and he knows you're good at logic too). He presents you with ten boxes labelled 1 through to 10. He tells you that inside one of the boxes is a prize. You have to open the boxes one at a time in the order 1 to 10. He also tells you that he absolutely guarantees that you will be surprised at which the box the prize is in when you open it.

Knowing that your friend is completely trustworthy and logical, you reason that it can't be in box 10, because if you had opened box 9, then you'd know that the prize must be in box 10; but that wouldn't then be a surprise. You also know your friend will be aware of that also. You then deduce that it can't be in box 9 by similar reasoning. And so on. So it must be in box 1; but, of course, that wouldn't be a surprise either.

So which box is the prize in?

100 and Nines

Express 100 using six 9s.

Mystery Message

Can you break the code and discover the mystery message?

USJDL PG NJOE
CZ
SBKFTI MBM

The grand prize is ... mmmm ... oh yeah, there is no prize.

Three Twos

Using three 2s, and only three 2s, how many different numbers can you write? ... and what are they?

How Old?

If you transpose the digits of Abe's age, you get Bill's age. The difference between Abe's and Bill's ages is twice Claude's age. Bill is ten times as old as Claude.

What color is the bear? ... oh wait ... wrong problem. What are the ages?

Looking for Five

Find a 2 digit number, with identical digits, such that when it is multiplied by 99, the product has a 5 as the 3rd digit from the left.

Racing Runners

Two runners compete in a race of considerable distance. The first runs for a period which is half his total time, then walks the remainder . The second runs half the distance, then walks the second half.

Both begin at the same time ... run the same speed ... and walk the same speed.

Who wins the race?

What if both racers walk first? With all other conditions the same, who wins?

Candles Burning

We have two candles of different sizes. The lengths and the thicknesses are different. The longer candle has a 3 1/2 hour burn time. The shorter candle has a 5 hour burn time. They are lit at the same time and burn for two hours. After the two hour burn, the candles are the same length.

What fractional part of the longer candles original length, is the shorter candles original length?

Who dunnit?

This one's a little bit different, but not too hard.

Blah, blah, a robber nicked something. Four suspects were interviewed (where have I heard this before?). Their statements were:

A: I wasn't in town at the time of the theft.
B: C is the culprit.
C: B's statement is false.
D: C's statement is true.

The robber's statement is false, the other statement are true. So, who dunnit?

Spiral Problem

Start with a square with a side length of one.
Divide it in half (left from right).
Divide the right half in half (top and bottom).
Divide the top half in half (left and right).
Divide the left half in half (top and bottom).
Divide the bottom half in half (left and right).
So on and so forth.
It creates a spiral.
The centre of each subsequent division is approaching a limit.
What are the coordinates of the point the spiral is moving towards?

-- Shaul

Family Members

Four male members of the Smith family went racing one afternoon at a local track. The racetrack was short and each one them had a go at breaking the record time of 19 seconds for one lap. None of them managed it but on a positive note none of them embarrassed themselves by taking longer than a minute to complete a lap. When the Stewart collection the lap times (to the nearest second) he revealed that there was at least five seconds gap between each racer. He also gave out a series of clues to see if they could guess their lap times:

He told Bill that he his time was exactly two thirds of Alex’s.

He told Calvin that two racers were precisely 20 seconds apart and that the 45-year old was not one of them

He told Derek that one of the family members older than him was exactly 30 seconds quicker than him.

He told the only member of the family who was not old enough yet to buy an alcoholic drink, that his time was double his age.

He told the 30 year old, that his lap time was not a prime number but one of the other three racers lap time was.

He told the 25 year old that he does not share either digit of his number (i.e. lap time) with another family member.

Can you work out which family member had which time?

-- Antn'y Jacobs

Horsing Around!

Cam and Chris left the same town, at the same time, to attend a TOM conference in the nearby metropolis of Puzzletown. One of the puzzlers travelled via horse, and the other drove a vehicle.

It became apparent:

That if Chris had travelled three times as far as he had, he would have half as far to ride as he had ridden;

and

That if Cam had travelled half as far as he had, he would have three times as far to ride as he already had.

Who rode the horse? ... and what color was the horse? (oops ... darn pain meds ... forget the color question).

Boats and a Buoy

Two boats, Knightmare's Couch and Chris's London Fog, leave the dock on a river simultaeously. Knightmare's Couch heads downstream, and Chris's London Fog upstream, both utilizing equal power. As they depart, a life bouy falls from Knightmare's Couch and floats with the river current. After an hour, both boats reverse course.

Which boat will reach the life bouy first?

Who Is Faster?

A man rows a particular distance on a river, with the current, and then rows the same distance against the current. A second man rows the same total distance, as the first man, on a lake where there is obviously no current.

Given that the two men are of equal rowing strength, which takes longer to complete the row?

Beer and Fish

Three friends were spending a Saturday afternoon in a small boat on a lazy stream. They anchored the boat under an overhanging tree at the waters edge. After baiting hooks, each man grabbed a cold brew from the cooler. After each had downed a few, Knightmare felt the urge from mother nature and stood to gain relief. He accidentally tipped the cooler and several beers disappeared into the murky water.

The beers which had remained in the boat, were then divided equally. After each drank four more, the total beers in the boat were equal to the number each had after the division.

How many beers had been divided after the cooler tipped?

Sharing Crayons

Three brothers shared 24 crayons. Each had a quantity equal to his age 3 years ago. A trade was suggested by the youngest brother ... that he keep half his crayons and divide the other half between his two brothers. Then he proposed, the middle aged brother, after receiving the crayons, do the same thing. To complete his proposal, the older brother, after receiving crayons from the middle aged brother, would perform the same sharing procedure.

After some discussion, the brothers agreed to the swap. Upon completion, each brother had 8 crayons.

What are the ages of the brothers?

Number 9

In the past I have friends ask me why "mind reading" tricks work. A particular one led me to notice (and prove) that if you take any integer and subtract from it any anagram of it (subtracting the smaller number from the larger number) that the result is divisible by 9.

Now you prove it.

6174

Take any 4 digit number which has at least 2 digits that are different (e.g. 1112 is OK).

Rearrange the digits to produce the largest possible number and the smallest possible number. Subtract the smaller from the larger one. After at most seven steps, you'll end up with 6174, and then you'll only get 6174 after that. Prove it.

e.g. for 6174 you'd do 7641 - 1467 = 6174

Sadly, this one's easily to find on the Internet, so please don't cheat. I've only looked enough to confirm it's there.

The Troll Bridge

A gentleman traveler came upon a rickety old bridge. As he started to cross, he awakened a troll who had been asleep on his versatile couch underneath the bridge.

"You there ... you dare to cross my bridge without permission!" growled the wart-ladened old troll.

Startled, the traveler responded, "I knew not that the bridge had an owner."

"Well ... now you know ... what do you have to say for yourself?"

"Kind sir, may I cross your bridge?"

The troll appeared to ponder the request. "Since you asked so politely ... you may ... and since I had such a restful nap on my couch, which was manufactured by Knightmare Couches, I will make you an offer. Every time you cross my bridge, I will double your money."

"That's incredible ... and I may cross as many times as I like?"

"Certainly," smiled the troll. "All you have to do is give me $24 each time you cross."

Ecstatic about his good fortune, the traveler crossed the bridge ... he checked his coins and sure enough, they had doubled. He laughed, and tosssed the troll $24. Again he crossed, his money doubled, and he paid the troll. He crossed a third time, his money doubled ...

"Oh no," exclaimed the un-suspecting traveler. "I have only $24 remaining in my purse ..."

"And it's mine!" yelled the troll.

The weary traveler paid the troll ... sad and broke, he continued on his journey.

As the troll lay upon his comfortable couch, he cackled with delight ... "Idiots ... they're all idiots".

How much money did the traveler have before enterring into the agreement with the mischevious troll?

Winners, losers and liars

This is probably my last on this theme.

A, B, C and D run in a race. When interviewed A, B and C made two statments each:

A: C won; B was second
B: C was second; D was third
C: D was last; A was second

If each told one true statement and one porky, who won the race?

Loan an Employee

Cam, Chris, and Ragknot are friends who have each started new companies. They talk frequently and decide to share resources when necessary. Since the companies are similiar in nature, the employees are actually able to move from one to another without loss of efficiency.

Cam's business started a little slowly, so he loaned Chris's company and Ragknot's company as many employees as each company already had.

In a few months, as economical conditions changed, Chris's company loaned Cam and Ragnot a number of employees equal to the number each already had.

Cam's and Chris's business really started thriving, in a few months, so Ragknot loaned each of his friends a number of employees equivalent to the number each already had.

After the last loan, each company then had 24 employees.

How many employees did each company originally have?

Emil the Mathematician

Emil is trying to PROVE that if you consider a set of size 2n+1, you can cycle through all the subsets of size n or n+1, by adding or deleting one element at a time.

Can you help Emil? ... he's a little senile and eccentric!

Painting a Fence - The Next Job

Chris and Zaux have decided to take on another fence paining job, as they did so well on the last job. They realise that they need some help, so they recruit Knightmare. How long would it take them to finish the job if Zaux can do it alone in 6 hours more, Chris 2 hours more and Knightmare in twice the time. I'm paying by the hour... minimum wage, mind...

- Karl Sharman

Who's who

Three men A, B and C are grandfather, father and son:

If C is the grandfather then B is the father.
If C is the father then B is the son.
If B is not the grandfather then A is the father.
If A is the son then C is the father.

Who's who?

More guilt

The following statements are all true:

If A is not guilty, then B and C are both guilty.
Either A is not guilty or B is guilty.
Either B is not guilty or C is not guilty.

Who is guilty?

Who Took the Scotch?

After the night of the imbibing competition at the tavern, the bartender noticed he was missing a full case of his most expensive single malt scotch. After analyzing and making a list of the suspects, he phoned each and requested he attend a meeting to offer input on future activities to be held at the tavern.

At the meeting, he explained the true reason each was summoned ... someone stole a case of expensive scotch.

Cam said, "I didn't take the scotch. I have never stolen anything. Knightmare took it.

Chris said, "I certainly didn't take it. I can afford to buy my own Scotch. Zaux knows who took it."

Karl said, "Not me ... didn't take it. I didn't know Zaux before a week ago. Knightmare did it."

Knightmare said, "I am not guilty. Zaux stole it. Cam is lying when he said I took it."

Zaux said, "I did not steal the scotch. Chris is the one. Karl can vouch for me ... he has known me forever."

The bartender said, "Gentlemen, I like all you guys ... that's why I didn't call the police. I'm a little confused right now ... but when I decipher these statements and determine who took my case of scotch, either you will pay for it, or I will contact the authorities. Good day!"

As the suspects were leaving the tavern, one of the bartenders employees who had been cleaning the kitchen area cam forth. "Hey boss, I was here the night of the competition ... please don't be mad, but I know who took the scotch. The problem is that all those guys are friends and I can't rat on one of them."

"Well, if you don't tell me, how will I find the truth?" exclaimed the bartender.

"I can tell you this", offered the employee. "I heard all their comments, and each guy told one lie."

Can you help the bartender decipher who took his case of expensive scotch?

Rational or not

If x and y are irrational, prove that x^y can be rational.

You only need to find one example to make the proof.

Who Done it?

The tiny little village of Nothinghappenshere was shocked at the early morning news. A murder had been committed. The body had been discovered by a jogger in the woods near town. The body was taken to the town doctor to be examined so that cause of death could be determined. The town constable had questioned the jogger, who found the body, hoping to gather clues as to what happened. The only real information the jogger could provide was that the victims digital watch had been struck during the assault and had stopped at that time. The jogger had scribbled the time displayed on a piece of paper which he handed to the constable. (below is a copy of the note):


After a frustrating morning, the constable contacted Solvz-it-All detective agency in a nearby town to help solve the crime. Two investigators, Cam and Chris, arrived to help. After questioning everyone in town, and determining that no outsiders had visited the village for at least 2 weeks, they came up with 4 suspects. The suspects, Karl, Knightmare, Wiz, and Ragknot, were summoned to the town hall where Cam and Chris questioned them. Here is the information and comments they gathered:



The suspect who admitted being in the woods at 3PM said, "Either Karl or Knightmare is a lawyer, and the other one is a grocer. I'm sorry ... my memory is just not what it used to be".



The suspect who arrived at the town hall at 5PM, to give his statement, said, "Karl has an occupation ... I believe it begins with "G", and neither Wiz nor I is a pharmacist".



At 8PM, another suspect arrived to provide information. "Either Knightmare or Wiz lives on my street", he volunteered.



The last suspect, who arrived at 9PM, said, "I am neither a pharmacist nor a geologist".



Detective Cam said this seems straightforward. His partner Chris cautioned, "Watch carefully, and lets reconsider all the comments and evidence ... something is not right!"



Help Cam and Chris find the person and occupation for each time, and most important ... WHO DONE IT?

Equals What?

(original posting of this problem was incorrect ... here is the corrected version)

492x04 = [3(230+y)]^2

Solve for x and y.

Twos and More Twos

You can express a number using only twos in following manner:(use 5 twos and any of the mathematical operators, plus exponents and parentheses)

1 = 2 + 2 - 2 - 2/2

5 = 2 + 2 + 2 - 2/2

7 = 22/2 -2 -2

and so forth.

Express the numbers 11 through 20 in this manner.

A Quite Simple Math Problem

Anyone can add single digits integers ... 5 + 4 = 9, 2 + 4 = 6, etc. Anyone can do this (even Ragknot ... heh heh ... don't tell him I said that).

So this is a quite simple problem ... simply add all the digits in the numbers from 1 to 1,000,000,000.

This is not like the famous problem a school teacher gave to her class to add all the integers from 1 to 100. Her class included the eventually famous mathematician Karl Friedrich Gauss, who at the time was 9 years old. He fairly quickly provided the correct answer of 5,050.

Our problem is a little different. Here's the start:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
In the next step, when we conssider 10, we do not add 10, but rather 1, making 46.
Next, we consider 11, which adds 2, making a total of 48.
Next, adding the digits in 12, we get 51.
And so so forth up to 1,000,000,000.

Should be easy ... anyone can add single digit integers.

Answer anyone?

Motorcycle Odometer

Knightmare was riding his Harley on a fairly long trip. He glanced at the odometer and noticed the mileage to be 15,951 (reading the same forwards and backwards). As he cruised down the highway, he thought ... I bet that won't happen again for quite a while. Exactly 2 hours later, he glanced at the odometer again and another palindromic mileage was dispayed.

How fast was the Harley going during those two hours?

Paint a Fence

it takes Chris three hours to paint a fence. it takes Zaux 6 hours to do the same job. How long would it take both of them together to finish the job?

-Knightmare

bag n balls

You have a bag with n balls. 50% are black, 50% white (n is even).

How many different ways can you pull out all the balls?

E.g.
n = 2 -> {BW, WB} = 2 ways.
n = 4 -> {BBWW, BWBW, BWWB, WBBW, WBWB, WWBB} = 6 ways

- steve brick

Ragknot Special

Arrange digits "0" through "9" into a 10 digit number, which when divided by "9" produces a palindromic quotient ( digits are the same from right to left, or left to right)

Solve this

WWWDOT - GOOGLE = DOTCOM

Realizing ofcourse that values of M and E could be interchanged.
No leading zero's are allowed.
it is => wwwdot minus google equal to dotcom

each letter is a number

It's My Billiard Cue

After the night of the Spirit's Competition at the local tavern, Knightmare, Cam, and Chris decided to go to Chris's house to play 5-card draw poker. They invited one of Chris's neighbors to join the game. More spirits were enjoyed during poker, and sometime around 2AM, the neighbor went home and everyone else crashed in the living room on sofas and chairs.

Upon awakening the next morning, Chris made coffee and stumbled outside to retrieve the newspaper. On his front porch was a nice leather case and note which read:

"Enjoyed last night ... thanks for the invite. Please accept this as payment of the money I lost in the card game." Chris opened the case to find a very nice, quite expensive looking 2-piece billiard cue.

When Knightmare and Cam awakened, he showed them the cue. The spirits of the previous evening had clouded everyones memory and a friendly discussion ensued as to proper ownership of the billiard cue.

Not intentionally, but because memories were foggy, each made one true and one false statement:

Knightmare said: 1. "the cue should belong to Chris" and
2. "It is certainly not mine"

Cam said: 1. "Chris has no right to it" and
2. "it should belong to Knightmare"

Chris said: 1. "yes, I seem to remember winning it" and
2. "Cam, it doesn't belong to Knightmare"

Please help these guys settle the debate as to who won the billiard cue during the poker game of the previous evening.

Spirits Competition

Karl, Cam, Chris, and Zaux are all lovers of spirits. One evening they are sitting in their favorite watering hole and a heated debate ensues over who can consume the most of their favorite poison. Chris suggests a competition for bragging rights. The bartender likes the idea (to increase sales) ... he agrees to keep the shots coming. With the first tray of assorted shots, he brings a pen and pad so the group can document their endeavors. Using an honor system, each one keeps a tally of his consumption. After 2 hours, the group agrees they have all had their limit. Being, a little bleary eyed, they turn in the information to the bartender to determine the winner. The bartender sets up a chart upon which to post the information ... being an extremely busy night, he posts information between drawing tap beer and offering snacks to all his customers. Although he gets all the info in the correct column, his hectic work pace causes him to get only one item in each column in the correct position.



Here's the incorrect chart:



--------------- NAME ---- SURNAME ---- SHOT TYPE



First Place ----- Karl ------Woozy ---------- Scotch



Second Place --Cam ------ Lighthead ------ Bourbon



Third Place ----Chris ----- Cantsee --------- Vodka



Fourth Place ---Zaux ----- Redeye --------- Tequila



A mutual friend, who had watched and enjoyed the competition, looked at the bartender's finished chart and said, "I watched the whole thing, this can't be right. I do know that:



* Zaux is one place above his friend who had Tequila

* The bourbon drinker is not above Chris

* Woozy is two places below Chris

* The bourbon drinker is one place above Lighthead"


The confused, and very busy, bartender offers free drink of choice, for the remainder of the evening, to anyone who can correctly rearrange the chart.

Are you thirsty enough to correct the chart?

Number Square Mystery

Look at this number pattern:

1---2---3

4---5---6

7---8---9

Your job, should you decide to accept it:

Rearrange the numbers such that the sum of every number immediately adjacent to each number is a multpile of the number.
For instance:

Look at 7 ... numbers immediately adjacent are 4, 5, and 8 ... their sum is 17 ... certainly not a multiple of 7. FYI ... I do not have the solution, so I will be solving with you.

Nation of Zox

The nation of Zox consists of five islands: Zog, Zod, Zob, Zop, and Zoz. The total population of all five islands is 750 Zoxians.

Using the clues below, determine how many Zoxians live on each island:

1. The smallest island has 1/10 as many Zoxians as all of Zox.

2. The largest island is Zod. The smallest island is not Zoz.

3. One island has 1/5 of the total population of Zox. Another island has 1/3.

4. Zob is one and a half times larger than one of the other islands.

5. Zop has 100 more people than the smallest island.

The Robbery

There are 4 suspects in a robbery: A, B, C , and D. Each makes a statement, but only one speaks the truth:

A. B did it.

B. C did it.

C. I did it.

D. Either A or C is the guilty one.

Who is the robber?

Baffling Numbers

---T --W--E--L--V--E

---T--W--E--L--V--E

---T--W--E--L--V--E

---T--W--E--L--V--E

---T--W--E--L--V--E

-+-T--H--I--R--T--Y

________________

---N--I--N--E--T--Y



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

Three Primes

Find three different two-digit prime numbers where the average of any two is a prime , and the average of all three is a prime.

The Infected Checkerboard

An infection spreads among the squares of an n x n checkerboard in the following manner. If a square has two or more infected neighbors, then it becomes infected itself. (Neighbors are orthogonal only, so each square has at most four neighbors.) For example, suppose that we begin with all n squares on a main diagonal infected. Then the infection will spread to the whole board.

Prove that you cannot infect the whole board if you begin with fewer than n infected squares.

Odd Streak of Heads

On average, how many times do you need to flip a fair coin before you have seen a run of an odd number of heads, followed by a tail?

The Lost Boarding Pass

One hundred passengers line up to board an airplane, but the first has lost his boarding pass and takes a random seat instead. Each subsequent passenger take his or her assigned seat if available, otherwise a random unoccupied seat.

What is the probability that the last passenger to board finds his seat occupied?

Losing at Dice

When six dice are rolled, the number of different numbers which can appear range from 1 to 6. Suppose that once every minute the 6 dice are rolled and you bet $1, at even odds, that the number of different numbers to appear will be exactly 4.

If you start with $10, roughly how long will it be on average before you are wiped out?

A Poorly Designed Clock

The hour and minute hands of a clock are indistinguishable. How many moments are there in a day when it is not possible to tell from this clock what time it is?

Summing to 15

Alice and Bob alternately choose numbers, one at a time, from the set:

1, 2, 3, 4, 5, 6, 7, 8, 9

The first to select 3 numbers whose sum is 15, wins the game.

If Alice goes first, it there a strategy which insures her win?

Lottery

Why would it be inadvisable to choose a simple set of random numbers like 1,2,3,4,5, and 6?

Wouldn't the odds of any set be equal??

First Odd Number in an Alphabetical list

Each number from 1 to 10^10 is written out in formal English (e.g. , "two hundred eleven", "one thousand forty-two") and then listed in alphabetical order (as in a dictionary, where spaces and hyphens are ignored).

What's the first odd number in the list?

Uses of Fuses

You are presented with two fuses (lengths of string), each of which will burn for exactly one minute, but not uniformly along its length.

How can you use them to measure 45 seconds?

Rolling All the Numbers

On average, how many times do you need to roll a die before all six numbers have turned up?

Sequencing the Digits

How many ways are there to write the numbers 0 through 9 in a row, such that each number, other than the left-most, is within one of some number to the left of it.

The Gambler's Ruin

At the beginning of play, gamblers A and B have m and n chips, respectively. Let their probabilities of winning be p for A, and q=1-p for B. After each play, the winner gets a chip from the loser, and play continues until one of the players is ruined.

What is the probability of A being ruined?

Up and away

Two balls of greatly different masses are dropped (almost touching) from a height of 1 metre. They fall through the same path, with the light ball following the heavy ball. After the bounce(s), how high will the lighter ball get to?

If you were able to cascade a series of balls together (with each upper ball being much lighter than the one below it), how many balls would be needed for the uppermost (lightest) ball to achieve escape velocity? Assume that escape velocity = 11 km/sec.

Assume that the balls have neglible diameter compared to 1 metre. Neglect air resistance and only make simplifying assumptions.

The Wrong Letter

An individual has written k letters to each of k different friends, and addressed the k corresponding envelopes.

How many different ways are there to place every letter into a wrong envelope?

My God..... It's full of stars

There are 4 men, Zaux, Wizard of Oz, Cam and Rajesh Lal, all buried up to their necks in the ground. They cannot move so can only look forward. Between Zaux and the Wizard of Oz is a brick wall which cannot be seen through. They all know that between them they are wearing 4 hats, 2 x black and 2 x white, but they do not know what colour they are wearing. In order to avoid being shot one of them must call out to the executioner the colour of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out.
There are no outside influences nor other ways of communicating. They cannot move and are buried in a straight line. So Zaux and the Wizard of Oz can only see their respective sides of the wall, Cam can see the Wizard of Oz, and Rajesh Lal can see the Wizard of Oz and Cam.

After 1 minute, one of them calls out.

Question: Which one of them calls out?
Question: Why is he 100% certain of the colour of his hat?

- Karl Sharman

Flavors

You are an entrepreneur trying to come up with a new flavor to excite the taste buds of the worlds population, and in the process reap the monetary rewards. You have chosen 6 beginning flavors from which to formulate your new flavor:

astringent, bitter, sour, pungent, saline, and sweet (each of these is a new unique flavor you developed)

Given that one test means either:

* selecting one of the 6 unique flavors as the new flavor
or
* combining an equal amount of 2 or more flavors to produce a unique flavor

How many tests are necessary to try all the possibilities?

The Monkey and the Coconuts

Five men and a monkey were shipwrecked on a desert island, and they spent the first day gathering coconuts for food. They piled them all together and went to sleep for the night.

One awakened and, wanting to avoid a fuss in the morning, decided to take his share. So he divided the coconuts into five piles. Having one coconut too many to make five equal piles, he gave the extra coconut to the monkey. After hiding his share, he made a single pile of the remaining coconuts and went back to sleep. (smart monkey - he also hid his coconut)

Each of the other four men did the same procedure, as the first man, at different times during the night. Each hid his share, gave one to the monkey to even the shares, and went back to sleep.

In the morning, each man awakened to find a much smaller pile of coconuts. No one commented on the reduced quantity, because each knew he was guilty.

How many coconuts were in the original pile? ( smallest quantity to satisfy the conditions)

Four Rowers and a Swan

Four rowers wish to cross the river by means of a boat that can only hold two men. The rower R1 needs one minute to cross the river alone, and the rowers R2, R3, and R4 need 2, 6, and 9 minutes respectively. Since the boat will hold only two men at a time, the rowers planned an optimum strategy for crossing the river. At the moment the rowers implement their plan, a swan starts to swim across the river at a speed of 60 feet per minute. The swan reaches the other side precisely at the moment the rowers complete their plan of getting all across the river.

What was the plan? Who rows with who?
How long did it take to accomplish the plan?
How wide is the river?

Two Cars and a Bird

Two cars, setting out from points A and B are 140 miles apart. They move toward each other on the same perfectly straight road, until they collide at C. Their speeds are 30 mph and 40 mph. At the very instant they start, a bird takes flight from point A heading straight toward the car which has left point B. As soon as the bird reaches the other car, it turns and changes direction. The bird flies back and forth between the two cars at a speed of 50 mph until the cars collide.

How long is the birds total flight path?

Meeting of Ships

Daily at noon, a ship departs from Le Havre bound for New York and conversely, another ship leaves New York bound for Le Havre. The crossing takes 7 days and 7 nights. During the passage to New York, how many Le Havre ships will the New York-bound vessel meet, with today as its date of departure?

Hungry Oxen

In 4 weeks, 12 oxen consume 3 1/3 acres of pasture land. In 9 weeks, 21 oxen consume 10 acres of pasture land. Assuming the grass grows at a uniform rate, how many oxen are required to consume 24 acres in a period of 18 weeks?

Sides of Two Cubes

The difference between the sides of two cubes is 6, and the difference in their volumes is 504.

Find the sides of the cubes!

Happy New Year

How many words can you make from the letters in the word 'Happy New Year'.

1. Keeping the sequence
2. Not keeping the sequence

and Happy New Year to all you ToM Puzzlers!

Stealing Wine

A dishonest servant takes out 3 pints of wine from a barrel and replaces them with the same amount of water. He repeats this theft twice, removing in total 9 pints and replacing them with water. As a result of this swindle, the diluted wine remaining in the barrel lost half of its former strength.

How much wine was in the barrel before the thievery began?