Monday, July 28, 2014

Brain Breaks Brain Teasers Math Riddles

Raymond Merrill Smullyan
(born May 25, 1919)
 is an American mathematician,
concert pianistlogician,
Taoist philosopher, and magician.
Student Brain Breaks Math Puzzles, Logic Puzzles, Math Riddles And Brain Teasers 

The Dark Bridge 
Once upon a time four students needed to cross an unlit bridge at night to get to the library. They only have one flashlight and 17 minutes to get there. The bridge must be crossed using the flashlight to see and can only support two students at a time. The 5th grader can cross in 1 minute, the 4th grader can cross in 2 minutes, the 1st grader can cross in 5 minutes and the kindergartner can cross in 10 minutes. How can they all make it to the library in time?

Once upon a time three report card envelopes are presented in front of you by your teacher. One contains a great report card with straight A's, the other two contain Bad report cards with all F's. You get to pick one of the report card envelopes. The teacher then shows you the contents of one of the other envelopes, which is a Bad report card. The teacher now gives you the opportunity to switch envelope choices. Should you switch?

The Story: Fox, goose and bag of beans
Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and rented a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases - the fox, the goose, or the bag of the beans.

If left together, the fox would eat the goose, or the goose would eat the beans.

The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

The Hardest Logic Puzzle Ever

It is stated as follows:
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no oare da and ja, in some order. You do not know which word means which.
 Clarifications, a single god may be asked more than one question, questions are permitted to depend on the answers to earlier questions, and the nature of Random's response should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

Bridge and torch problem

Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Person A can cross the bridge in one minute, B in two minutes, C in five minutes, and D in eight minutes. When two people cross the bridge together, they must move at the slower person's pace. The question is, can they all get across the bridge in 15 minutes or less?

The problem: Students and cannibals
Three exchange students and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, if there are 
exchange students present on the bank, they cannot be outnumbered by cannibals (if they were, the cannibals would eat the exchange students). The boat cannot cross the river by itself with no people on board. And, in some variations, one of the cannibals has only one arm and cannot row.

Twelve balls
You have twelve balls that weigh the same, except for one. This ball may be lighter or it may be heavier than the other eleven. You are given some scales to balance balls against each other. How do you discover the rouge ball, and whether it is heavier or lighter, with only three weighings?

You are standing next to a well, and you have two jugs. One jug has a content of 3 litres, and the other one has a content of 5 litres. How do you measure out 4 litres ?

Knights And Knaves
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:
Knights who always tell the truth.
Knaves, who always lie.
Normals who sometimes tell the truth and sometimes lie

Assume you meet one of these inhabitants, and he tells you "I'm no knight". What type inhabitant is he ? Or is it impossible to determine ?

A man is digging a hole

A man is digging a hole, and is one third of the way through When he is finished his head will be twice as far below ground as it is now is above ground. If the man is 5'10, how deep will be the hole be when he has finished?

Cross a bridge
There are 4 men who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side.

It is night. There is one only one torch. A maximum of 2 people can cross at one time. Any party, who crosses, either 1 or 2 people, must have the torch with them. The torch must be walked back and forth, it cannot be thrown, etc. Each man walks at a different speed. A pair must walk together at the rate of the slower man’s pace.

Man 1: 1 minute to cross. Man 2: 2 minutes to cross. Man 3: 5 minutes to cross. Man 4: 10 minutes to cross.

The King is about to die
The King is about to die. He sends messengers throughout the land seeking for the 3 smartest people. Finally 3 are found. He gives them a task to see which one is the wisest. He tells them, "I will seat you in a triangle so that each of you faces the other two. After you are blindfolded I will paint a dot on each of your foreheads. Each dot will be red or green so that there can be any combination of red and green dots. When I remove the blindfolds each of you must raise your hand if you see _any_ green dots, i.e. 1 or 2 dots. As soon as you have figured out what color your own dot is, lower your hand and tell me."

So he seats them, blindfolds them, and then paints a green dot on all three foreheads. When the blindfolds are removed, all three hands go up. After a long pause, one hand comes down and the man says.

"Your highness, I have a green dot."

Bow And Arrow

A bow and arrow cost 21 gold pieces. The bow cost 20 more than the arrow. What is the price of each ?

Warriors Age
A warrior, when asked his age, replied he was 25 years old not including Saturdays or Sundays. What was his real age?

A pirate ship captures a treasure of 1000 gold coins. The treasure has to be split amongst the five pirates : 1,2,3,4 and 5 in order of rank. The pirates have the following important characteristics: Infinitely clever
Starting with pirate 5, they can make a proposal of how to split the treasure. This proposal can either be accepted, or the pirate is thrown overboard. A proposal is only accepted if, and only if, the majority of pirates agree on it.

What proposal should pirate 5 make ?

The Pirate game

There are 5 rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.

The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.

The pirate world's rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. In case of a tie vote the proposer has the casting vote. If the distribution is accepted, the coins are disbursed and the game ends. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.

Pirates base their decisions on three factors. First of all, each pirate wants to survive. Second, given survival, each pirate wants to maximize the number of gold coins he receives. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal. The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal.

What is the sum of numbers from 1 to 100?

You've got a 10 x 10 x 10 cube made up of 1 x 1 x 1 smaller cubes. The outside of the larger cube is completely painted red. On how many of the smaller cubes is there any red paint?

You are given a 3-gallon jug and a 5-gallon jug. How do you use the jugs to get 4 gallons of liquid exactly?

A windowless room has 3 light bulbs. You are outside the room with 3 switches, each controlling one of the light bulbs. If you can only enter the room one time, how can you determine which switch controls which light bulb?

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