Yishai Shimoni's good riddles page
A good riddle is one that anyone can solve but most people don't. This means that you have the necessary tools to solve it but you're somehow blind to see how to use them. A question that requires knowledge in Geography, Biology, etc. is not a riddle, but a quiz. It can still be fun, but it is not the main goal of this site. Below I give a list of riddles, and at the end several quizzes. You should think about each one for a while, and if you are totally stuck follow the hints link. There, read only one hint at a time and think some more. Finally, I also provide a link to the solution. In the solution I try to explain the logic leading to the correct solution, not only the technical details.
Enjoy.
Enjoy.
The King and the Hats
A king is angry with his ministers and calls them up to the cabinet room. "Tomorrow at dawn I will align you in a row and I will put a hat on each of your heads", the king tells them. "I will go from the back of the line and ask you what color is the hat on your head. Your answer must be one word: red, green, or blue. If you say anything else you die. If you are wrong you die. You cannot know the order you will be in. You will be able to see the hats of every person ahead of you, but not the ones behind you, and not your own hat. You will hear the answers of each person and the consequences of their answer. You will stay here under guard tonight. Good night". What should the ministers do to minimize the number of deaths? (bonus question: what should they do in case of a mistake?)
hints solution
hints solution
The Blind Go Player
A blind man is given n go chips - they are round and smooth discs, each chip is white on one side and orange on the other. He is told that m<n of the chips are showing orange and the rest are showing white. His challenge is to separate the chips into two sets containing an equal number of orange chips.
(this riddle courtesy of Mukesh Bansal)
hints solution
(this riddle courtesy of Mukesh Bansal)
hints solution
Half a Bottle
Two people walk in the desert and find a transparent bottle of water completely full (e.g. a mineral water bottle). The bottle is not symmetrical in any direction. They want to make sure they each drink exactly half a bottle of water. How?
(this riddle courtesy of Antonina Mitrofanova)
hints solution
(this riddle courtesy of Antonina Mitrofanova)
hints solution
How to cut the cake?
The participants of a party wish to eat a cake (for simplicity let's assume a loaf-shaped cake, where you cut off slices, not wedges). They have a plastic knife that cannot harm anyone. How can they distribute the cake so that no-one can complain about the size of the piece they got compared to others?
hints solution
hints solution
Fair Inheritance
On a sad occasion, the parents of three brothers die without leaving a will. The three brothers meet and need to distribute the inheritance so that they all get a share that they think is fair. How can they do this?
hints solution
hints solution
Diagonal of a rectangle
There is a rectangle consisting of M-by-N identical squares. A straight line passes from the top left corner to the bottom right corner. Through how many squares does the line pass?
(this riddle is courtesy of Maria Rodriguez Martinez)
hints solution
(this riddle is courtesy of Maria Rodriguez Martinez)
hints solution
12 balls
A criminally insane billiards salesman gives a man 12 identical looking billiard balls. "I lost my explosive billiard ball, so one of them may be explosive" the salesman tells the man. "But don't worry, if it is in there then it weighs slightly more... or is it slightly less...?". He also allows the man to use a balance scale 3 times to identify the ball. Can it be done? How?
hints solution
hints solution
Pirate Ship Treasure
A pirate ship with 100 highly rational, enlightened, and bloodthirsty pirates on board comes upon a treasure of 100 gold coins. Being pirates, there is a very clear hierarchy between them. The highest ranking pirate (let's call him the captain) makes an offer on how to split the loot. Being rational and enlightened pirates, they all vote on the suggestion. Being bloodthirsty, if there is a majority against the decision then the captain is killed, the second in command becomes captain, and the process continues until a suggestion is accepted. What proposal should the captain make?
The only assumptions are: 1. A pirate prefers anything to dying. 2. The pirates are rational. 3. All things being equal a pirate doesn't mind if his captain dies.
Bonus riddle: what if the captain doesn't vote on his own proposal?
hints solution
The only assumptions are: 1. A pirate prefers anything to dying. 2. The pirates are rational. 3. All things being equal a pirate doesn't mind if his captain dies.
Bonus riddle: what if the captain doesn't vote on his own proposal?
hints solution
Quizzes:
Beer Buddies
This is a game theory quiz.
Two math students (call them Andy and Brian) go to a pub to drink some beer. To decide who pays for each round, they each choose a positive integer (Andy chooses a and Brian chooses b) and writes it on a napkin. They then compare napkins. If a>b then Andy buys the beer, unless a=b+1, in which case Brian buys two rounds (and vice versa). Is there any strategy for choosing the numbers that guarantees no losses in the long run? What is it?
hints solution