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?

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)?

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.

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).

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.

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

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?

Fashion Show

Three models - Miss Pink, Miss Green, and Miss Blue - are on the catwalk. Their dresses are solid pink, solid green, and solid blue.

"It's strange," Miss Blue remarks to the others. "We are named Pink, Green, and Blue, and our dresses are pink, green and blue, but none of us is wearing the dress which matches her name."

"That is a conicidence," says the woman in Green.

What color dress is each woman wearing?

Fair's Fair

Bill Fair's gaming booth at the state fair had an interesting game. On the counter in front of him were four overturned cups. Each concealed the same number of balls. On each cup was a statement about the number of balls underneath. From left to right the statements were:

one or four
two or four
two or three
one or two

Only one of the statements was correct.

Could you win a prize at Bill Fair's booth? How many balls were under each cup, and which statement was true?

Piggy Banks

Three nickels and three dimes are distributed among three piggy banks such that each holds two coins:

one bank is labeled 10 cents
one bank is labeled 15 cents
one bank is labeled 20 cents

The banks are mislabeled according to the coin distribution ... is it possible to accurately re-label the banks by shaking only one of them until a single coin falls out? If so, explain!

A Christmas Gift

It's Christmas, all merry and joyful
In me, the goodies are plentiful
If you know what's in me,
you'll get three,
with another for free
A third is yellow, with spikes for protection,
A third is red, with its seeds like perspiration,
A third is purle, with bitter peels as protection,
They're for Jesus' favourites, they say
But they're even on gingerbread house roofs that play
They're all sweet and tasty
But they might give you cavities, ouchy
They come from country of islands
near the most populous land
So go ahead and guess
or all you'll get is a mess!!!

So, what goodies are inside me??

(Merry Christmas
and a Happy New Year
to everyone ^^)

Flags, ropes, roofs - oh my!

This is a riddle of two flags on flagpoles on houseroofs
You have a rope to assist you
You are only human so there're no poofs
You can't tie the rope on flage poles and pull across
Because then you would surely fall
You can't reach across roofs
Because you're just not that tall
You can't swing on the rope
Because then you will meet your death
You can't be on the ground
Because then you will be in enemy's grasp
If you can make a road
Then you'll cross without a yelp
Mind that glue gun in your pocket
Because it will come to help
Oh and with infinite amount of rope
How would you get to the other flag?
But don't worry if you have no hope
Because it won't cost you an arm nor leg
Try this, if you can, without your glue.

(sorry, I'm not really a poet)

Number Logic

Two perfect logicians S and P are told that integers x and y are such that:
1 < x < y and that x + y < 100.

S and P are then given the values x+y and x*y respectively and privately. S and P know they have each been given the sum and product respectively. They then have the following conversation:

P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.

Given that they spoke the truth, what are the two numbers?

Dec 24, 5: 10 AM. I made a significant modification to the conditionals for x and y. The place I found this sneakily used computers in deriving the solution. Unfortunately, my modifications altered the situation too much and invalidated the conversation between S and P.

In fact x < 10 and y < 20; but S and P don't know that. Unfortunately, I doubt that extra info is going to usefully simplify the problem solution. So apologies in advance if this one has a high labour requirement.

How many Children

"I heard some children playing in your backyard," said Jones. "Are they all yours?"

"Heavens no," exclaimed Smith. "My children are playing with friends from three other families in the neighborhood, although our family happens to be the largest. The Browns have a smaller number of children ... the Greens have a still smaller number ... and the Blacks family is the smallest of all."

"How many children are there all together?" asked Jones.

"Let me put it this way," said Smith. "There a fewer than eighteen children, and the product of the number of children in each of the four families
happens to be my house number ... which you saw when you arrived."

Jones began figuring on his notepad ... he then said, "I need more info ... is there more than one child in the Black family?"

As soon as Smith responded, Jones smiled and then stated the number of children in each family.

How many children were in each family?


- Zaux

Liquid Assets

At the reading of their father's will, 3 sons of a wine merchant learn their father left them:

7 full barrels of wine
7 half barrels of wine
7 empty barrels

The will stipulates that each son receive the same number of full barrels, half full barrels, and empty barrels.
The lawyer, reading the will, exclaims "Oh my goodness ... how is this possible?"

- Zaux

Dice Drama

There are six squares marked 1, 2, 3, 4, 5, 6. You are invited to place your money as you wish on any one square. Three dice are then thrown.

The Rules
-------------
If your number appears on one dice only, you get your money back plus the same amount.
If two dice show your number, you get your money back plus twice the amount you placed on the square.
If your number appears on all three dice, you get your money back plus three times the amount. Of course if the number is not on any of the dice, the operator gets your money.

Now, you might reason: the chance of my number showing on one dice is 1 : 6, but since there are three dice, the chances must be 3 : 6 or 1 :2, therefore the game is a fair one. Of course this is the way the operator of the game wants everyone to reason, because it’s quite fallacious. But is the game favourable to the operator or the player, and, in any case, just how favourable is it ?

Trio is Back

Tom, Dick and Harry went fishing, having agreed to share the catch equally. After a successful day, they put the catch on the boat deck to be divided up later, had a big party, and went to sleep. In the middle of the night the Tom wakes up, feeling ill, and decides to go home with his share. But he sees that the catch can't be divided evenly into three because there is one fish too many. So he throws the extra fish into the lake, takes his share, and goes home. A little later the Dick wakes up, also feeling sick, and decides to go home with his share. Not realizing that Tom has already left, he also sees that the catch can't be divided equally because of an extra fish. He throws the extra fish into the water and departs. Finally Harry wakes up, ill as well, and unaware that his friends have gone, counts the fish, finds one extra, throws it away and takes his share.

The question is, What is the smallest number of fish that the fishermen could have caught during the day?

On Logic

1) All of the humankind, other than my footmen, have a certain amount of common-sense;
2) No one, who lives on barley-sugar, can be anything but a mere baby;
3) None but a hopscotch player knows what real happiness is;
4) No mere baby has a grain of common-sense;
5) No engine-driver ever plays hopscotch;
6) No footman of mine is ignorant of what true happiness is.

What logical conclusions you can make from here ?

Sum Problem

In a group of 10 people, each one is asked to write sum of the ages of the other 9. The sums form the 9 element-set (82, 83, 84, 85, 87, 89, 90, 91, 92). Find the ages of the youngest and the oldest in the group and the ages of the two persons with the same age.

Lies and Statistics

An independent survey conducted in a large school indicated the lying habits of the students were as follows
category / percentage of students / percentage of lies told of all statements made): (A) Truthful students / 10% / 0%;
(B) Students who seldom lied / 20% / 20%;
(C) Students who evenly lied / 40% / 50%;
(D) Students who frequently lied / 20% / 80%;
(E) Students who were liars / 10% / 100%.

The same group of students were given a multiple choice questionnaire and were asked to indicate the category (A, B, C, D, or E) which they belonged to. Obviously students would indicate their category, depending upon their nature – eg: All truthful students would put themselves in category A, but Liars would never indicate category E.

The problem is, what would be the percentages of students in various categories as self indicated by the students? Further if a second self-assessment survey is conducted asking the students whether they had truthfully answered the first self assessment survey having only two categories (T) Told the truth, and (F) Lied, what would the results tell in percentage terms?

Eight Women

Eight women, including Ms Irwin, went into a department store to buy one item each. Each went directly to the floor where the item she needed was sold, made the purchase, and left immediately. Two items were sold on each of the store’s four floors (first floor through fourth floor). Can you find each woman's full name (one was named Gracie), the item she bought, the floor it was sold on, and, in the cases of the women who left the first floor and how each arrived at and left the floor of their purchase?

(1) The three women who used the escalator at least once were Eilsa, Ms Kring, and the woman who bought the oil painting;
(2) The dress and the radio were sold on the same floor;
(3) The three women who used the elevator to get both up and down were Dielia (who bought the lamp), Ms Loing, and the woman who bought the radio;
(4) Ms Nielson got her item on the fourth floor;
(5) Claria did not buy the ring. She and Beth went to the same floor;
(6) The three women who did not use the elevator at all were Eilsa, Ms Miller, and the woman who bought the coat;
(7) Helen used both the elevator and escalator;
(8) The woman who bought the linens went down by escalator;
(9) Ms Jonas and Alice took the elevator to their different floors. Flo and the woman who bought the books took the escalator up together, since they were going to the same floor. All four rode down on the elevator at the same time and met Ms Perkins as she entered it on the ground floor;
(10) The only woman to use the stairs was Ms Owens, who did not make her purchase on the third floor.

The Mall Problem

8 small store occupy the new Great Mall in the shape of a 3x3 grid (with the centre square being an open area) numbered 1 to 8 clockwise from the top left square. They are a bookstore, flower shop, frozen yogurt shop, futon shop, painting and wallpaper store, pizza, photo studio, and shoe store. The 8 proprietors include five women – Eimma, Francis, Ruith, Vecke and Ziina – and three men – Alberto, Georgio and Lukio. The proprietors’ last names are Cole, Gallo, Hanley, Jackson, Klein, Martinez, Riley and Silver. Can you match each shop’s number with the full name of its owner and the kind of shop he or she runs?

(1) On the northern wall are (in no particular order) Eimma’s store, Lukio’s store, and Hanley’s store;
(2) Riley’s shop is situated directly opposite the florist’s, and isn’t adjacent to Cole’s place;
(3) Klein’s shop and the pizzeria aren’t both on the eastern wall;
(4) Francis and Gallo are the only two women who don’t have corner stores;
(5) Neither Alberto’s store nor Jackson’s is on the southern wall;
(6) Georgio’s shop is adjacent to the Bookstore;
(7) On the western wall are (in no particular order) Vecke’s shop, Martinez’s shop, and Ziina’s futon shop;
(8) The pizzeria and the frozen yogurt shop occupy opposite corners of the mall;
(9) The florist is adjacent to the photo developer;
(10) The paint and wallpaper store is adjacent to both Ruith’s shop and the shoe store;
(11) Lukio’s shop is adjacent to Silver’s.

"That's all the information I have Holmes" said Watson.

Urgent Letter

A military car carrying an important letter must cross a desert. There is no petrol station in the desert, and the car's fuel tank is just enough to take it half way across. There are other cars with the same fuel capacity that can transfer their petrol to one another. There are no canisters or rope to tow the cars.

How can the letter be delivered?

Duelling dilemma

There are there duellists. One is very good, one is average and the third is rubbish. What is the best strategy for each of them to maximise their chances of surviving in a three way duel. Assume that they are standing at the corners of an equilateral triangle with sides of length 30 feet. The exact detail isn't important, I'm just trying to cause the focus to be on the real logic problem presented.

This is a classic. I haven't disguised it. I haven't even Googled it.

The Traveller

A truck travels down the hill at 72 mph, on the level at 63 mph, and up the hill at only 56 mph. The truck takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes. What’s the distance between the two towns?

Ace, King and Queen

Place a Ace (A), a Queen (Q) and a King (K) on three slots in a row like AQK (A on extreme left, K on extreme right). Reverse the position of the cards (ie, KQA) in the least possible number of moves. In a valid move, a card can be moved either left or right into an empty slot or placed onto a card of a higher rank. (eg, a Q can be placed on a K, but not vice-versa). Also, only the top card of the stack can be moved. Now, what is the least number of moves required if:
(a) there are only three slots?
(b) there is an empty slot to the left of the Ace?
(c) there is an empty slot to the right of the King?

Save the Robber

Five robbers steal 1000 gold coins and devise the following method to divide them:

The youngest robber has to present a plan to divide them. The plan is accepted only if majority of robbers accept it. (Two out of four won’t do.) If the plan is rejected the presenter of plan is shot and the next older robber gets a chance. So what plan should youngest robber present to save his life?

Pi Problem

A friend of mine is a crammer and a bragger. He claims he remembers the value of pi up to 100 places by heart. The trouble is I do not. And I am marooned with him on an island with no books, computers, mobile or calculator. The question is, how can I verify that the 100 digits he is rattling off is not gibberish?

The Rope Problem

Assume, we lay a rope tightly around the Planet and then elongate this rope by just 1 meter and then evenly distribute this additional length around the whole equator.

What is the extra length of the Rope required ?

40 in the balance

Using a balance scale and four weights you must be able to balance any integer load from 1 to 40. How much should each of the four weights weigh?

Curious Contract

A visitor at a Motel makes a curious contract with the landlord. He wants to pay for his board and lodging by giving one link of a gold chain he possesses, on a daily basis. As the chain has 63 links, this would permit the visitor to stay for 63 days. That’s 63 cuts.

However, later in his room as the visitor prepares to sever the first link, he realizes that fewer cuts would mean less work. And, on reflection, comes to the conclusion that the number of links he actually would have to cut is far smaller than he had initially imagined. So what is the minimum number of links that he must cut to enable him to carry out his regular daily payment schedule?

Running order

Say there are 333 marathon runners. Each is randomly handed a number (1 to 333) to wear. What is the probability that the first three to finish will be wearing numbers that are in decreasing (not necessarily sequential) order?

Coin tossing (yet another)

You flip two coins simultaneously. If one coin is heads, what is the probability that the other coin is heads?

Cross that bridge

Three people (A, B and C) need to cross a bridge. A can cross the bridge in 10 minutes, B can cross in 5 minutes, and C can cross in 2 minutes. They have a bicycle and any person can cross the bridge in 1 minute using it. All three men and the bicycle start together on one side of the bridge. Only one person can use the bicycle at a time. The bicycle can be mounted and dismounted anywhere. All three men can be crossing together. What's the shortest time that all three men can cross the bridge in?

Turning heads

You are sitting at a table. On the table are 887 coins. 113 of the coins are heads up, the rest are tails up. You have to create two sets of coins. Each set must end up with the same number of heads facing up. That sounds easy. Unfortunately, it is totally dark and you can't feel which side of a coin is which. How can you do it?

More Prisoner Problems

Out of three prisoners scheduled to be put to death, Tom, Dick, and Harry, one of them will be pardoned. Tom asks the warden to tell him the name of one of the others who will be executed. As the question is not directly about Tom's fate, the warden obliges — either naming the other prisoner to be executed, in case Tom was too, or secretly flipping a coin to decide which of the remaining names to give Tom if Tom is the one being pardoned. Assuming the warden's truthfulness, there are now only two possibilities for who will be pardoned: Tom, and whichever of Dick or Harry the warden did not name. Did Tom gain any information as to his own fate, that is, does he change his estimate of the chances he will be pardoned?

If the warden says "Dick will be executed" and Tom could switch fates with Harry, should he?

Prisoner Problem

Consider a prisoner who’s about to be put to death but is promised his freedom if he draws a silver ball from one of two identical vase. He’s allowed to put 50 silver and 50 gold balls among the two vase any way he likes. The vase are then going to be shuffled around out of his sight and he has to pick one vase and draw one ball at random from that vase.

So how does the prisoner maximize his chances of survival? If he puts an equal number of silver and gold balls into one of the urns, the other urn would also contain an equal number of silver and gold balls, and thus the probability of his drawing a silver would be one in two. Can these chances be improved? If so, how?

Marbleous 2

You have a collection of bags of marbles. Some of the bags contain marbles of weight 10 g, the other bags contain marbles of weight 11 g. Your mission is to determine which bags are which in one weighing. You have a suitably accurate weighing machine. I won't state the other assumption, in case I give too much away.

This is probably another familiar golden oldie.

Series Story

Till how many terms can you carry on the following series:

The series starts with A3, B1, C1, continues with G2, H2, J2, K2, and so on . . .?

Warren Buffet and Bill Gates

There is a round table conference. Warren Buffet is the richest person while Bill Gates sitting on his right has one dollar less then him. And the person on Bill’s right has two dollars less than Warren. And so on. Warren feels game and gives 1 dollar to Bill. He in turn gives 2 dollars to the person on his right. And so on.

But at one stage some one says, "Now I don’t have 1 dollar extra to give to the person on my right." However, he also says that he has 101 dollar more than him. How many dollars did Warren have initially and how many people were there?

Elementary Arithmetic

In the introduction to an early literary work on elementary arithmetic, the author looking back over his life, muses: "I was once x years old in the year x cube. I am now x square years of age and in another x years my only son will be y years of age in the year y square."

In what year was the author of the manuscript born?

Return to WowDVDFilm

A few days ago, there was a ToM that presented a problem where 8 variables could be valued as single digits 0 to 9, but there could NOT be a repeating value. Such as W could not equal D. The eight variables were W,O,D,V,F,I,L, and M.
My question is how many combination would there be? Review the WOW ToM - and figure out the number of combinations are possible with this set of eight variables, and is there a trick here? If so what?

You're kidding!

A and B have the following conversation:

A: How old are your three kids?
B: The product of their ages is 36.
A: I still don't know their ages.
B: The sum of their ages is the same as your house number.
A: I still don't know their ages.
B: The oldest one has red hair.
A: Ah, now I know their ages.

How old are the kids?

Assume the kids ages are an exact number of years.

Red faced children

A teacher tells a group of children that at least one of them has a red face. ‘Step forward if you have a red face’, he says at intervals, until... What happens next?

Assume that the children are clever enough to behave logically, they aren't disobedient and they can see each others faces, but not their own.

Happy Birthday

I expect everyone knows this one, but it's better than nothing.

In a random group of 23 people, there is a slightly better than a 50% chance that at least two of them share the same birthday. How is that possible?

How big would the group need to be to get the chance of a shared birthday up to at least 95%?

Discard all leap year complications. Assume each birthday is equally likely. Only consider the day and month, not the year of birth. It is not a trick problem.

Family Ties

Boy says: "I have as many brothers as sisters."

His sister says, "I have twice as many brothers as sisters."

How many of brothers and sisters are there in the family ?

The bare facts of the naked truth

I hope this one isn't too well known.

A man died and went to heaven. When he got there he found that everyone was naked. A man and a woman walked over to greet him. The (newly dead) man said to them, "Hello Adam, hello Eve".

How did he know who they were?

A Circle Mystery

From Harry Potter and the Deathly Hallows:
"Which came first, the phoenix or the flame?"
"...a circle has no beginning," Luna Lovegood once cleverly said.

But really, does a circle have no beginning?
I mean, there has to be something that begun the circle,
or else there would be no circle at all..........

What do you think?

A fox, hen and a basket of corn

This is a very old logic puzzle. Maybe in will be fun for some newbies.

A man had a fox, a hen and a basket of corn. He came to a river. There was a canoe there, but he could only take himself and one other thing in the canoe. If left unattend, the fox would eat the hen, or the hen eat the corn.

How did he manage to get himself and all three items across the river?

Alice and Bob

Today is Alice's birthday. She turned 24. Alice is twice as old as Bob was when Alice was as old as Bob now. How old is bob now ?

Gates Foundation

If Gates have 5 billion dollars spare cash and he start giving away $ 500 every minute, how long would it take him to give away all the spare ?

Straight Time

There is a time between seven and eight when the two hands of the clock makes a straight line. Would you know ?

The Rhetorical Question

"If it takes 1 & 1/2 men, 1 & 1/2 days," says Punnish strutting about in imitation of his master, "to pot 1 & 1/2 geraniums in 1 & 1/2 pots, how many will 2 & 1/2 men pot in 6 days?"

He is rather shocked to hear Pembish answering this rhetorical question from with in the greenhouse.

What, incidentally, is the answer ?

Acceleration - unit conversion

Ok, I give one more. I think these may be to hard for many people.
K = (100 * 60 * 60 *60) / (2.54 * 12 *5280)

Since this is acceleration, the units will be a length per time * time

_____ per _____ * ____ * K = ______ per _____ * _____

and K = approx 134.21

This is a unit conversion I never used before, so I verified the answer here.

http://www.onlineconversion.com/index.htm

Conversion factor 3

This is "Flow", as in volume per time. (Length^3 / time)

K = (100*100*100*60*60*24)/(2.54*2.54*2.54*12*12*12*43560) = approximately 70

______ per _______ * K = ______ per _______

Socks Story

John Bayleaf often wears odd socks, and this afternoon was no exception. He tells me that he keeps all his socks in a bottom drawer and that when he dresses he removes a pair at random.

If he has four pairs of socks: one black, one white, one red and one blue. How many days per week on average will he be found wearing a matching pair?

Deaf Spy

A deaf spy is sent to spy on an air field. He takes a room in the boarding house of Mrs. Oldham. Every now and then, and at random, he makes an excuse to go up to the attic room in order to watch the airfield with his opera glasses untill he sees an airplane. He then immediately makes a note of this in his report and goes back downstairs.

Back in Oblivia, Funkov goes through the spy's report. "It is worse than useless," he says. "We already know that every single hour, day and night, exactly one plane lands, refuels and leaves in a perfectly regular fashion. And yet this report states that he finds 11 times as many planes landing as taking off."

"Hm," says his colleague, Khatzov. "That makes sense. We can get some useful information out of it."

What information can he had from these facts ?

The White and the Snakeshead

There are two types of Zirconian fritillary: the White and the Snakeshead. Both grow to a height of 45 zonks. The White, however, grows at a rate of one zonk in the first tink, two zonks in the second tink, three zonks in the third zink, etc. The Snakeshead variety is more interesting, it grows in such a way that its height increases by three zonks in first two tinks, by six zonks in second two tinks, nine zonks in the third tinks, etc. The both germinate(from zero height) at the same time.

Which of the two will be fully grown first?

Clock Crypt

"Well I was proceeding down Lettsby Avenue," said Police Constable Klepto, "and had just turned around into Silent Mews."

"And what time was this" asked Queen's Counsel Casey,

"Well I don't remember, but the hour hand and the minute hand were exactly on minute divisions of the clock face and the minute hand was exactly 13 minute divisions ahead of the hour hand."

Luckily Dr. Chronos was in the court. What time did he suggest the recorder record?

Quogmoth

It is the first anniversary of the formation of the Zircon Zargo team. Each player, being a clone, secretly buys all the other players a ticket to Quogmoth, a revolutionary Ballet of spheres except for the goalkeeper who, being forgetful, doesn't buy any. As a result 1,183 dinglies are spent.

How many men are there in a Zargo team and how much are the tickets ?

The Penny Farthing Bike

"My father was also a tireless man - an inventor," said Punnish, scarcely able to contain his amusement as Pembish tried to look disapproving. "His penny-farthing bike, if you pardon the term, had metal wheels of circumference 60 and 135 centimeters respectively."

How far would you have to push this machine forward before both the wheels were again in the same position relative to the road ?

A Short Career.

2 friends met up after a long time. One of them was a brilliant scholar and the other an engineer. They decided to have some coffee. During the course of their conversations, they began to talk about their days at college.
"So, I heard that you played for the state cricket team for a year after college" said the engineer.
"Yes" replied the scholar, and wanting to test his friend, he said, "In my total career as a state player, I played n games and made (n+1)(2^n+1 -n-2) / 4 runs totally, and in the kth math I made k.2^n+1-k runs"
"Oh!" said the engineer, "that was a short career."

Can you find how long did the 'short' career last?

The Waitress

"That reminds me," said the waitress, "of a time when I was giving three guests after dinner coffee and I called out from the kitchen to see how they wanted it. Back came the reply that two wanted it with cream, two with sugar, two with rum and none with all three.

For a moment I was at a loss to how to prepare those three cups. But not for long."

Now Johnny, You tell me how did I prepare them ?  

Time Stop

"Well, in that case, what time is it now?" asked the striker, noting that the wall clock said 2:00 PM.

"Time to be off," replied Chronos, picking up his cuckoo clock from the seat beside him and tucking it under his arm. "It's Thursday, and I have an appointment this afternoon in town. My seven-hour clock stopped this morning and I have to take it to the repair shop. Look it says 1:00 now." With this he swept out, making a timely exit.

When had the time stopped in his clock ?

What is wrong with this equation?

What is wrong with this equation?

1^10 + 2^10 + 3^10.... + 10^10 = ((10*11)/2)^10

Hair Problem

What is the probability that, at least two people in the world have exactly same number of hairs ?

Tom, Dick and Harry

Tom, Dick and Harry are in prison. One of them has been randomly selected to die in the morning, and the other two will be set free. Their guard knows which one will die, but none of the prisoners does. The guard is under strict instructions not to divulge the identity of the doomed man.

Tom is desperate for any information beyond the fact that his probability of death is one in three. He begs the guard to throw him an informational bone. Finally, to shut him up, the guard agrees to reveal only the following: the name of one of Tom's fellow prisoners who will be set free rather than killed. The guard then says that Dick will be set free.

After receiving this information from the guard, what is the most accurate calculation Tom can make of the probability that he is the doomed man?

Thanks for your time
-- Josh Mudie

Birthday Puzzle

Bob and Betty has five children - Polly, Jolly, Molly, Lolly, and Dolly

Eldest Polly is born on 1st of January. Next is Jolly, born on 1st of February. 1st of March is again the scene of birthday celebration in their house. What is the probability of it not being that of molly's ?

Oh yes the sum of the ages of the five children equals product of their ages.

Temperature Twist

"What's the temperature in Fahrenheit, required for the chemical reaction?" asked the student.

"Its a two digit number in Celsius and if you switch the place you get the temperature in Fahrenheit" explained the professor.

"That is still ambiguous !" said the student.

"You are smart ! Choose the pair with more evens !"

Toaster Ovens

A small-appliance manufacturer finds that it costs $9,000 to
produce 1000 toaster ovens a week and $12,000 to produce
1500 toaster ovens a week, and $21,000 to produce 3500.
How many toasters per week would they need to produce
for the average unit cost to be $4.00?

Birth Date

Suppose there are 40 students in a class, and suppose they are all born in the same year. What are the chances that two students have same birth date ?

Clock Work

When Sylar opened a clock to service, he saw that the big wheel has 21 teeth and the small one 7 teeth. He immediately knew how many times it takes for small wheel to rotate to circle around the big wheel. Do you ?

* Can you believe there is a standard formula for this !

Fifty Cents

A drink machine has three options Coke, Pepsi and Random. Each drink is fifty cents. A friend tells you that the machine is faulty and that the buttons are never correct.

How much money would you need to spend to know which buttons deliver which drinks?

Dinosaurs

On the island of Triassic, the Dinosaur population, thought to be near extinction, has expanded enormously. We know now two facts about them:

1> There are 400 Dinosaurs
2> No Dinosaur has more than 50 wrinkles on his body

From this we can deduce that there must be two Dinosaurs with the same number of wrinkles?

Alpha, Beta, and Gamma

When Professor Nova's triplets were born, he nicknamed them alpha, beta, and gamma, and, so as not to confuse them, had their clothes monogrammed with these words to make them identifiable at a glance.

One day, Alpha said to the brother wearing the word Beta, "Do you realise we are all wearing the wrong words today?"

Who was wearing which words ?

Pensioner

John is an old pensioner. Reversing the digits of his age this year and doubling the answer gives his age next year. How old is John ?

True Lies

"The other one says he is john !" A voice came from the corridor. Two guys were standing there, John who always lies and Jim who always tells the truth.

Who do you think said those word ?

Clock Work

At precisely 6:00 AM the angle between the minute and hour hand of a clock is 180 degrees. To the nearest second, what time will it be when the angle between the two hands is again 180 degrees.

The Oil Problem

An oil well being drilled in flat prairie country struck pay sand at an under ground spot exactly 21,000 feet from one corner of a rectangular plot of farmland, 18,000 feet from the opposite corner, and 6000 feet from a third corner.

How far is the underground spot from the fourth corner ?

The Secret Password

A man wants to enter a private club, but the main door is guarded by a doorman who only lets people in who know the right password. The man hides in the bushes near the door and listens.

One patron approaches the doorman, who says, "12."
The patron replies, "6," and the doorman lets him in.

Another patron approaches the doorman who says, "6."
The patron replies, "3," and the doorman lets him in.

Thinking he has the code figures out, the man approaches the doorman.
The doorman says, "8," and the man replies, "4."
"I'm sorry sir," the doorman says, "This is a private club and only members are allowed."

What did the man do wrong?

Posted by Sammy's Dad on October 14, 2008.

Bermuda Triangle

The Journal of the Paranormal reported the following,

It happened on the morning of March 20, 1862 The Ship "Mulan" vanished at sea!

"Mulan" was 50 foot long merchant ship transporting industrial spare parts and headed towards Miami. The night before the incident the crew was relaxing, on the fore deck playing cards, smoking or looking at the Florida coast. The captain was quietly filling his log book in his cabin when he noticed the beams of the lighthouse. But "Mulan" never reached her destination and nobody heard any more from the ship or her crew. Surprisingly no evidence was found until now which could have explained this sudden disappearance.

"Something is not right here, Dr. Watson" said Sherlock Holmes, "Think !"

I Told You I Was Ill

A hypochondriac drinks his medicine until there is only one third left in the bottle. He then dilutes the rest with water until the bottle is two thirds full.

"This would be too light" he said to himself and tops the bottle with a mixture twice as strong as the original medicine.

He is still not sure if the resultant mixture is stronger or weaker than the original one, and by how much. Are you ?

Last Year

What was the last year in which someone could have been born, in order to live in a year which was the square of their age ?

Einstein's Sphere

An Incredible Sphere was found in the laboratory of Einstein. A cylindrical hole, 6 inches long has been drilled through the center of the solid sphere. Remaining volume of the sphere was needed to solve the puzzling equation, written on the black board.

Can you help?

Books and Dates

An Author writes a book every two years. when his seventh book is published, the sum of the years in which they were all published is 13,804. In which year were his seven books published?

The wrong answer is : It cannot be found !

Rubik's Cube Solution

A Rubik's Cube is considered solved when each face has the same color of cubes. How may possible solutions are there for a Rubik's Cube

It's Murder, Watson!

The facts are these my dear Watson

"One member of the family murdered another member, the third member witnessed the crime, and the fourth member was an accessory after the fact." said Holmes.

On the scene, Inspector Lestrade was found, who added the following.

• Accessory and the witness were of opposite sex


• The oldest member and the witness were of opposite sex


• The youngest member and the victim were of opposite sex


• The accesory was older than the victim


• The father was the oldest


• The murderer was not the youngest

Hah ! cried Sherlock Holmes. Lestrade, still confused, what about you ?

Miles per Hour

If an electric train is going west at sixty miles an hour and the wind is blowing from north at thirty miles an hour, in which direction will the smoke from the engine blow and, at what Miles per Hour ?

Nancy and Sluggo

Sluggo meets a new friend Irma at Nancy's party, where all were, either Truth Tellers or Liars. Irma tells Sluggo that she has overheard a conversation in which a girl revealed her identity, saying she is a liar. Now sluggo is thinking, Is Irma a Liar or a Truth teller ?

What will you tell, if Sluggo ask you ?