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. Puzzles: Logic Puzzles. Start by introducing the students to the Liar and Truthteller families.
Then pose the first puzzle: You meet two people, Adam and Alec. Alternatively: Student: I think Adam is a Truthteller. The teacher resists giving the next conclusion, but does validate the thinking so far.
Then you meet Alex and Ali. Now you meet Antoine and Ashley. Ariel and Ben come by. Can you tell what family Ariel is from? David and Devon pass by. Elizabeth and Ellie are next. Elizabeth makes exactly one statement, which might be true, or it might be a lie. This is tough! Gregory and Hannah show up, and Hannah makes one complicated statement. John and Jennifer happen by. You meet Josh and Karina in the garden.
Harder puzzles: Kaitlyn and Lorna walk up to you. Melissa and Michael are both doing their homework when you arrive. If X was false, A would have to be a liar to say it. But then the statement "A would say X" would be true, and A couldn't say it.
If A was a truthteller, then "A would say X" would be false, and again, A couldn't say it. Once you've pinned down a few of the people, look at the remaining clues, and see what they tell you.
The most important rule: have fun, and if you know people who like this kind of puzzle, tell them about this page! Skip to content. By Michael Hartley This is a page of logic puzzles. I've made a "logic puzzle generator" that generates puzzles like these. Here's one:. Would you like a New Puzzle? A Harder Puzzle?
An Easier Puzzle? If you like what you've just read, sign up for this site's free newsletters: Monday Morning Math : A weekly email of fascinating math facts - how math works in everyday life. There are 7 same as the number of people possible hat colors. You know the seven possible colors.
I may place any number of each color e. You will be able to see everyone else's hat, but not your own. At the exact same time no communication after your hats are on you will guess the color of your hat. If any of you get it right, you all win. If you all get it wrong, you all lose. You now have time to come up with a strategy before I place the hats.
How do you ensure that you win? 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. How do you loop the string around the nails? The original version: There are nine stones.
Eight weigh the same amount, and one weighs slightly more than the others. You have a balance that will tell you if the left side weighs more than the right. Using the balance only twice, determine which is the heavy stone.
The balance problem on steroids: There are 12 stones, one of which weights a different amount from the others. You do not know whether it is heavier or lighter than the others. Using the balance three times, figure out which stone is different and whether it is heavier or lighter. You have a rope that is feet long. You can tie it in different ways and can also cut it.
You are on a cliff that is feet tall. There are rings to tie the rope to at the top and at the ledge. How can you get down? There are pirates. They have 10, gold pieces. These pirates are ranked from most fearsome 1 to least fearsome To divide the gold, the most fearsome pirate comes up with a method e.
The pirates then vote on this plan. The pirates are perfectly rational. Yes, I said that twice - it is important. You are the most fearsome pirate. How much gold can you get without being killed? There are mathematicians including you! Soon, I will enter and you will all line up such that you can see everyone in front of you, but nobody behind you. I will then place hats on each of yours heads. Each hat may be either black or white. You will not know what color hat you or anyone behind you in line is wearing.
I will then ask each of you what color hat you are wearing, starting from the back of the line and moving to the front starting from the person who see's everyone's hat color but his or her own, and ending with the person who sees nobody's hat color.
Now, before I enter and place the hats, come up with a strategy to ensure that 75 people live. Can you do even better? Draw seven distinct points on a piece of paper such that regardless of which three are chosen, at least two will be exactly one unit e. As far as I know, there is only one way to do this. An ant is in one corner of a room shaped like a cube. It wants to go to the opposite corner.
What is the shortest path that the ant can take, and how long is it? I place 8 coins on a table in a line with random sides up. You can look at the coins and then flip one coin. You leave and your friend enters. Come up with a strategy so that your friend can determine which coin you flipped. You have a square cafeteria tray with four quarters on it - one in each corner. Again, we are in a dark room. You do not know which quarters have the heads side up and which have the tails side up. Your goal is to flip over any coins you want and then ask if they are all heads.
If they, are then you win. If they are not, then I rotate the tray randomly and we repeat the process. Can you ensure that you will eventually win? Do not physically do this - it will ruin it. There are two quarters on a table. One is glued in place, the other is adjacent to it. If you roll the quarter that isn't glued around the one that is glued until it reaches the position it started from, how many degrees will it have rotated by?
When I say "roll around" you can pretend the edges of the quarters are like gears. Some people find "how many degrees will it have rotated by" to be ambiguous so here's what I mean: If it starts with the head facing up and moves until the head is facing down, that is degrees. If the head rotates from up to down and all the way around to up again, that is degrees.
Once you are convinced you know the answer, try it. There is a duck in the middle of a perfectly circular pond radius 1. There is a fox running around the outside of the pond at speed 1.
The duck is injured in a way that it can only take off from land. How slowly can the duck swim in order to still be able to make it to the edge of the pond without the fox meeting it there? The fox can only run around the pond.
They are both points. The duck has no constraints on the derivative of its velocity. You have two identical glasses, filled to the same level. One has water in it and the other has wine. You take a teaspoon of the wine, pour it into the water, and mix them up. You then take a teaspoon of the water with a little wine in it , pour it into the wine and mix it up. Is there more water in the wine, or more wine in the water?
If a car is traveling at 60 miles per hour, what part is stationary? What part is going miles per hour? Bob flips fair coins. Alice flips What is the probability that Alice gets strictly more heads than Bob? You're in a boat with a big rock, in a swimming pool. You toss the rock overboard. What happens to the level of the water in the pool?
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