Guess a number

Probability Level 2

Alice thinks of a natural number between 1 and 10,000 (inclusive). Bob must guess it. Each time Bob makes a guess, Alice tells him whether it is too small, too big, or correct. If it is not correct, Bob guesses again.

How many guesses does Bob need in order to correctly identify Alice's number?

Clarification: It is not enough for Bob to figure out Alice's number. He must actually say it. That is, Bob's last guess must be the right answer.


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