Interesting Riddles for TAS Course in Cryptography
Riddle 1: General Code
Consider our class of 11. One wants a security system such that any three of us can initiate the coffee break, but no two of us can. The password is a triple of three numbers, say (a,b,c). How do we assign information to the 11 people so that any three of us know (a,b,c) but no two of us know (a,b,c)?
Riddle 2: Pirates of the Cryptobean
A man on island 1 wants to send an engagement ring to his girlfriend on island 2. Each has a lock and the corresponding key. Some friendly pirates (who have a box) will freely transmit anything in the box back and forth as many times as desired; however, they will take and keep anything in an unlocked box. How can you get the ring from island 1 to island 2?
Riddle 3: Mathematicians in a Row
100 mathematicians are in a row; the last sees all 99 people in front of her, the second to last sees the first 98, and so on. Each person will have either a white or a black hat placed on their head. The hats are not independently placed – the choice depends on the strategy the mathematicians adopt. First the 100th person speaks, then five seconds later the 99th, then five seconds later the 98th, …. When it’s your turn to speak you say either ‘white’ or ‘black’; for each person who says the color of their hat correctly, the mathematicians gain another million dollars, while for each incorrect color the team loses one million dollars. Remember, whatever strategy is chosen is known to the person choosing the hats. What is the largest number of hats you can ensure are correctly identified?
Riddle 4: Three Hats and a Strange Probability
Three players enter a room and a red or blue hat is placed on each persons head. The color of each hat is determined by tossing a fair coin, with the outcome of one coin toss having no effect on the others. Each person can see the other players hats but not his own.
No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a $3 million prize if at least one player guesses correctly and no players guess incorrectly. If even one person speaks incorrectly, the team loses $3 million. If they play optimally, what percent of the time do they win?
Riddle 5: Safe Generals
You have 7 generals and a safe with many locks. You assign the generals keys in such a way that EVERY set of four generals has enough keys between them to open ALL the locks; however, NO set of three generals is able to open ALL the locks. How many locks do you need, and list how many keys does the first general get, the second,