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Brain Teasers

These Brain Teasers are guaranteed to have you banging your head against the wall ! No mathematical knowledge whatsoever is required to solve this riddles Clicking on 'Solution' for a puzzle pops up a solution window like this. All solutions will appear in that window. You can then re-arrange the main window and the solutions window to appear on your desktop separately. This way, you can have a permanent solutions window that is refreshed when you view a new solution without disturbing the main window.

The Puzzles (Difficulty rating 1 Easy - 4 Difficult indicated by )

The answer to Question 2 is:

A. B
B. C
C. A

The first question with correct answer B is:

A. Question 3
B. Question 1
C. Question 2

The only answer you have not chosen yet is:

A. A
B. B
C. C

Four couples attended a party. One couple was you and your spouse; another was Pat and Chris. Some people shook hands with one another, but nobody shook hands with oneself or with one's own spouse.

After the party, you asked each person (except yourself) how many different people the person had shaken hands with. Each person replied with a different number--and each person's reply was truthful.

You shook hands with Pat. Did your spouse shake hands with Pat? With Chris? How did you reach that conclusion ?

Our Princess is in a quandary. Her wicked Uncle has decreed that she must marry one of his sons Tiny Tim, or Midget Mike. She must say one statement. If that statement is true, she must marry Tim. If it is false, she must marry Mike. What did she say to ensure her single status and her continued quest for sexual gratification ?

Three people check into a hotel. They pay £30 to the manager and go to their room. The manager suddenly remembers that the room rate is actually £25, not £30, and gives £5 to the bellboy to return to the people. On the way to the room the bellboy reasons that £5 would be difficult to share among three people so he pockets £2 and gives £1 to each person. Now each person paid £10 and got back £1. So they paid £9 each, totalling £27. The bellboy has £2, totalling £29. Where is the missing £1?

How quickly can you find out what is unusual about this paragraph? It looks so ordinary that you would think that nothing was wrong with it at all and, in fact, nothing is. But it is unusual. Why? If you study it and think about it you may find out, but I am not going to assist you in any way. You must do it without coaching. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour.

Your brand new home has a problem. On the top floor are three standing lights. On the ground floor are three switches which control the lights, presently all in the "Off" position. You don't know which switch controls which light, except that there is a one-to-one correspondence. You're down on the ground floor and want to label the switches but you want to do it in as few trips up stairs as possible. What is the minimum number of trips it takes ? 

Imagine you are on island and the following facts are true:

No inhabitant has exactly 154 hairs.

There are more inhabitants than there are hairs on the head of any one inhabitant.

What is the largest possible number of inhabitants of the island ?

A man (we'll call him Steve) said to his mate "All men are liars". Assuming that a liar always lies and someone who is not a liar always tells the truth, is Steve a liar ? And what can you tell about men is general ?

As in the original Knights And Knaves problem, imagine you are on an island. The inhabitants look the same from the outside, but differ from inside (their truthfulness). We distinguish the following types:

A man and a woman may only marry if they are both Normal, or one of them is a Knight and the other one is a Knave. Now you meet Mr. and Mrs. Bloggs who tell you the following:

Mr.A "My wife is not normal"

Mrs A "My husband is not normal"

What types of people are Mr. and Mrs. Bloggs ? Or is it impossible to tell ?

Three men are buried in the sand all facing the same way with their heads above ground. Each man has a hat placed on his head selected from a bag containing 3 red hats, and 2 black hats. The man at the back is asked what hat he is wearing. He replies "I do not know". The middle man is asked what hat he is wearing. He replies "I do not know". The man at the front is then asked what hat he is wearing. He replies "I am wearing a red hat". How did he know ?

Four men are buried in the sand all facing East. Between the front man and the man behind him is a 10 ft high brick wall.

Each man is given a hat. There are four hats in total, 2 are black, 2 are white. If a man guesses his hat colour correctly, all are free, otherwise all are beheaded. After a few seconds, the middle man of the three behind the wall shouts out the colour of his hat correctly. How did he know ?

The three wisest sages in the land were brought before the king to see which of them were worthy to become the king's advisor. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits.

Led blind-folded into a small room, the sages were seated around a small wooden table as the king described the test for them.

"Upon each of your heads I have placed a hat. Now you are either wearing a blue hat or a white hat. All I will tell you is this- at least one of you is wearing a blue hat. There may be only one blue hat and two white hats, there may be two blue hats and one white hat, or there may be three blue hats. But you may be certain that there are not three white hats."

"I will shortly remove your blind folds, and the test will begin. The first to correctly announce the color of his hat shall be my advisor. Be warned however, he who guesses wrongly shall be beheaded. If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom."

With that, the king uncovered the sages' eyes and sat in the corner and waited. One sage looked around and saw that his competitors each were wearing blue hats. From the look in their eyes he could see their thoughts were the same as his, "What is the color of my hat?"

For what seemed like hours no one spoke. Finally he stood up and correctly named the hat on his head. What colour was it, and how did he know ?

• Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim.
• Eight years ago, Mary was half as old as Jane will be when Jane is one year older than Tim will be at the time when Mary will be five times as old as Tim will be two years from now.
• When Tim was one year old, Mary was three years older than Tim will be when Jane is three times as old as Mary was six years before the time when Jane was half as old as Tim will be when Mary will be ten years older than Mary was when Jane was one-third as old as Tim will be when Mary will be three times as old as she was when Jane was born.

You are teacher organising a straight knock-out competition for your school in the computer game FIFA 2000. 864 pupils that have entered the competition. What is the total number of games played in the competition (assuming that some pupils will get a bye in the first round) before the winner is found ?

(taken from "Mathematical Diversions" by Hunter and Madachy)

I was there one Sunday and we had the usual business of his clock. When the radio gave the time at the hour, the Ormolu antique was exactly 3 minutes slow.

"It loses 7 minutes every hour", my old friend told me, as he had done so many times before. "No more and no less, but I've gotten used to it that way."

When I spent a second evening with him later that same month, I remarked on the fact that the clock was dead right by radio time at the hour. It was rather late in the evening, but Tom assured me that his treasure had not been adjusted nor fixed since my last visit.

What day of the week was the second visit?

The moderator takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the moderator's pocket and the two on her own head. He asks them in turn if they know the colors of their own stamps: A: "No" B: "No" C: "No" A: "No B: "Yes" What are the colors of her stamps, and what is the situation?

Two logicians place cards on their foreheads so that what is written on the card is visible only to the other logician. Consecutive positive integers have been written on the cards. The following conversation ensues: A: "I don't know my number." B: "I don't know my number." A: "I don't know my number." B: "I don't know my number." ... n statements of ignorance later ... A or B: "I know my number." What is on the card and how does the logician know it?

We've all seen magic squares where all rows and columns add up to the same number, but here's two grids with a difference :