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hat problem
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Say the king is bored and decides to play a game with 10 people. The king has 10 types of hat and randomly gives those hat to those 10 people (the number of each type of hat is not fixed, so everyone could have same or distinct hats). The goal of the game is for at least one person to guess their own hat type but before the game starts, they are allowed to communicate a strategy. After they have decided their strategy, they are then taken into a room where hats will be assigned and any sort of communication will be disallowed (including moving around, signling, etc). The king then waits a bit and after a short period of time snaps his finger, when all 10 people need to declare their guesses at the exact same time.
fun logical puzzle
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Say there are 1000 bottles of water and one of them is poisoness. A rat dies in exactly 10min after drinking one drop of poison(which means however many bottles you mix with the poisoness one, a rat still dies from drinking the resulting solution). Now, if you have only 10min, how many rats (min)to you need to find out which one is poinsoness.
An interesting math problem
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I came across this interesting problem in the 2024 Alibaba Global Mathematics Competition, the released solution for part one uses lie theory, which is probably the simpler and more intuitive way but there is another more brute force direct approach (way longer too, this one took me ages to come up with leaving me no time for the rest of the problems lol), so I thought I share it here.