Here is one for the brainy ones. Impossible brain teaser, can you do it? Have happy monday.
The Number Game: Alice and Bob are on a game show. Each is secretly told a whole, positive number. They are told the two numbers are consecutive, but neither knows the other person’s number. For example, if Alice is told 20, she does not know if Bob was told 19 or 21. And if Bob is told 21, he does not know if Alice was told 20 or 22. The point of the game is to guess the other person’s number. The game works as follows.
–Alice and Bob cannot communicate with each other, and they are not allowed to plan their strategy either.
–The two are in a room where a clock rings every minute.
–After the clock rings, either player can call out a guess of the other player’s number, or they can stay silent.
–The game continues until Alice or Bob makes a guess. After the first guess is made, the game ends.
–Alice and Bob win $1 million each if the guess is correct, and they lose and get nothing if the guess is incorrect.
How should Alice and Bob play this game to have the best chance of winning? Each knows the other person is perfect at logical reasoning.
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