But these special families, the Liars and Truthtellers can be trusted always to lie or always to tell the truth, depending on their family. You meet two people, Adam and Alec. What about Alec?
If students have no idea, suggest that they just guess about the speaker. Student: I think Adam is a Liar. If Adam is lying, then… What? Teacher: Right. Student : Well, if he lied, then he has to be a Liar. 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! You reach a fork in the road. A sign explains that in one direction is Heaven and the other is Hell. Each path is blocked by a Guard. The sign goes on to say that one of the guards will always lie and the other will always tell the truth, it does not say which guard is which. We assume that the guards do know which path leads to where. You may ask one question of only one guard in order that you can determine, with certainty, the way to Heaven.
What is that question? Before reading the answer can I interest you in a clue? There are lots of set ups for this puzzle. There is a prison with inmates. The warden strikes a deal with them.
There is a room with a light in it controlled by a light switch. Each day, the warden will take a random prisoner to that room. At some point, a prisoner must say "We have all been in the room! If he or she is wrong, then all will never be set free. The initial state of the light is not known on or off. Talking is allowed ahead of time, but not after the process begins. Also, the process will begin on a random day, so you do not know if you are the first in or not. You are a prisoner.
What plan do you propose in order to ensure that you will gain your freedom? 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. So, as a visitor to this strange world, you once meet a knight who tells you "I'm a day-knight and it's night".
Since you forgot to wind up your watch a few days ago, you don't know the time. But can you tell from this sentence, whether it's day or night? And can you tell, whether the knight is a Day-knight or a Night-knight? Hope you like the two riddles. I'm currently trying to figure out, what the title of that book was. When I found it, I'll tell you. Deborah Smith has objected to Stephan's line of reasoning:. Contact Front page Contents Algebra Impossible.
What is what? A puzzle of identical twins Following is an excerpt from B. Smullyan Suppose there are two identical twin brothers, one who always lies and the other who always tells the truth. I received a letter from Brad Crane : There is a similar puzzle to the one you put on your webpage. It goes like this: Suppose there are twin brothers, one which always tells the truth and one which always lies. Just in case you want to try to solve it, I'm putting in space here. Scroll to answer question below.
Enjoying your page as always, Brad Crane. I have a much simpler solution to Brad Crane's problem. Just ask him a question which you already know the answer to! Ask him, "Do you exist? Hi Alexander. I had to write to tell you that Stephan Hradek's line of reasoning has a flaw. He said, "If he is an inaccurate liar he will believe that he is an accurate truth teller since he is inaccurate in his beliefs , but then he will lie and say no.
Hradek is forgetting is that he will also be incorrect in his belief of his existence, he will have to say yes. And, yes he would have to be insane.
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