Find any solution that works - do not worry about how long it will take. The prisoners will be taken in randomly: over an infinite amount of time, they will all enter the room an infinite number of times.
Bonus: how long will it take for you to be freed? You have a very big urn, and pebbles numbered with the natural numbers 1, 2, At time step 1, you put pebbles in the urn.
At time step 2, you take out pebble 1. At time step 3 you put in At time step 4 you take out pebble 2, etc. If you did this an infinite number of times, how many pebbles would be left in the urn?
Hint: The limit as the number of iterations goes to infinity may give a different answer. Try to think about this one without using math at first. There is a rubber band attached to a wall. The rubber band is one meter long, levitating horizontally away from the wall. When I say "go", it will start stretching so the end moves at 10 meters per second.
It stretches infinitely. The stretch is uniform e. There is an ant starting where the rubber band connects to the wall. It walks at.
Will the ant ever reach the end of the rubber band? If so, how long will it take? What if the rubber band doubles in length every second? A woman and her husband attended a party with four other couples.
As is normal at parties, handshaking took place. Of course, no one shook their own hand or the hand of the person they came with. And not everyone shook everyone else's hand. But when the woman asked the other 9 people present how many different people's hands they had shaken they all gave a different answer. Question this is NOT a trick! You have two very resilient dinosaur eggs.
They will absorb a certain amount of force with no negative consequences, but at some point they will crack. If they don't crack, no damage is incurred. You're on a story building. You have 20 trials you're allowed at most 20 individual egg drops and 2 eggs. Is it possible to devise a testing strategy that guarantees to tell you at exactly what floor the eggs will break? If after your first trial dropping an egg off of the balcony on one floor of the building , if the egg does not break, then you have 19 trials remaining and two eggs.
If the egg breaks, then you still have 19 trials remaining, but only one egg left. How few trials do you need? Let this number be k. Using k trials, can you solve a story building?
How about ? You work with Jane. You know that she has two children. One day you meet one at a boys' camp, and it is a boy. What is the probability that she has two boys? Where on the Earth can you walk a mile south, a mile west, and a mile north, and end up exactly where you started?
Hint: There are infinite places: find them all! What is a shape defined by a mathematical equation that has infinite surface area, but finite volume? There are two empty bags. You have 50 black and 50 white pebbles. You must put all of the pebbles into the two bags. A coin will then be flipped. If it is heads, you discard bag A.
If it is tails, you discard bag B. From the remaining bag, you reach in and randomly select a pebble. If it is white, you win - black you lose. How should you put the pebbles in the bag? Does it make a difference? This problem is hard. If this is your first look at this page, I recommend skipping it.
There are a countably infinite number of mathematicians in a room. Each has a black or white hat placed on his or her head. Color selection is random. Each mathematician can see the color of everyone else's hat, but not his or her own.
At the same moment, with out communicating with each other, all must guess the color of his or her own hat. What strategy could the mathematicians use to guarantee that only a finite number guess incorrectly?
The mathematicians may talk before the hats are placed in order to agree on a strategy. You may assume the axiom of choice.
Toggle navigation. Publications Logic Puzzles Teaching. Logic Puzzles This is a collection of logic puzzles. Four Card Code You select five cards from a standard 52 card deck no jokers and place them on a table. The Othello Problem You are in a completely dark room.
The 7 Hats Problem You are in a room with 7 or any other number greather than 3 friends. Hanging a Picture You have a framed painting the kind with a string coming out of the top left and attached to the top right that you want to hang on the wall using two nails, such that if you remove any one nail the painting will fall, but with both nails in the wall it will not fall.
Scales On Steroids The original version: There are nine stones. The Mountain Climber You have a rope that is feet long. The Perfectly Logical Pirates There are pirates. Black and White Hats There are mathematicians including you! Ant in a Room An ant is in one corner of a room shaped like a cube. The Four Quarters Problem You have a square cafeteria tray with four quarters on it - one in each corner.
The Two Quarters Problem Do not physically do this - it will ruin it. The Duck and the Fox There is a duck in the middle of a perfectly circular pond radius 1. Water and Wine You have two identical glasses, filled to the same level.
Car Parts If a car is traveling at 60 miles per hour, what part is stationary? Coin Flip Contest Bob flips fair coins. How many meters does Rooney beat Robin by? Difficulty Popularity Adam is one of the finalist in an IQ championship.
As the final test, he is provided with two hourglass. One of them can measure eleven minutes while the other one can measure thirteen minutes. He is asked to measure exactly fifteen minutes using those two hourglasses. How will he do it? Fifteen minutes can easily be measure using these two hour glasses. Step 1: He will start both the hourglass.
Step 2: The moment the eleven minute hourglass is empty, he will invert it. Step 3: When the thirteen minutes hourglass is empty, he will invert the eleven minute hourglass. In step 3, we will have counted thirteen minutes. In this manner when it is reversed when the thirteen minute hourglass is finished, it will have two minutes of sand left.
This time when the sand finishes, he will have measured fifteen minutes. Difficulty Popularity A perfect number is defined as a positive number integer which is equal to the sum of its positive divisors excluding the number itself. Difficulty Popularity Can you win this chess game in one move. One day two are going together and a god appeared in from of them.
The God grant three wishes to Bheem and one to Dhuryodhan. Dhuryodhan replied smartly 'Give me twice of whatever Bheem ask for'. For 1st wish Bheem asked the god 'Give me a room full of money'. Soon Dhuryodhan gets two room full of money. Teacher: And do we know anything about Alec? Student: I think Adam is a Truthteller. If Adam is telling the truth, then… What?
Student: Wait! People — adults and students — who are new to these puzzles often get stumped at this point. Especially if they are not confident about their reasoning, they may attribute the contradiction to bad reasoning. But instead of recognizing the correctness of their thinking, people who are not used to this kind of problem can, at this point, feel confused. Teacher: Right! People in the Liar family always tell lies. Never, not even by accident, do they ever tell the truth. The Truthteller family is just as trustworthy.
You can depend on them to tell the truth, the whole truth, and nothing but the truth, always. The tough thing is that there is no way to tell these families apart just by looking at them. So, you have to be logical. The king of a far away land decided on the perfect way to try his prisoners. The prisoner would have to choose between two rooms, one of which contains a great banquet and the other of which contains a tiger.
If he chooses the former, he gets to dine at the banquet, and is let free; if he chooses the latter, the tiger gets to dine on him! The king designed this ordeal as a test. The king put signs on the doors of the rooms, but the signs posed a puzzle. If the prisoner reasoned logically, he could figure out which room to choose, saving his life, and giving him a great banquet, too!
If you were the prisoner, which door would you open assuming, of course, that you prefer eating to being eaten? Choose well.
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