A Search Game

A Search Game

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The formulation and partial solution of a hide-and-seek game. The hider chooses an integer from 1 to n; the hunter makes a guess, and is told whether he is too high or too low. The process is repeated until he has guessed correctly. The payoff is the expected number of guesses. Possible practical applications include the problem of correctly weighing an object within expected number of weighings on a balance scale playing against nature.