Misha thought of a number not less than 1 and not more than 1000. Vasya is allowed to ask only such questions that Misha can answer with "yes" or "no" (Misha always tells the truth). Can Vasya determine the guessed number in 10 questions

#
Strangely enough, this problem has something in common with problem $\underline{102982}$.

## Solution

Vasya will first ask if the number is greater than 500. Then, whether it is greater than 730 or less than 250, depending on Misha's answer to the 1st question, and so on (each time the distance from the number in the old question to the number in the new question is halved. For example, let's say Misha thought of the number 183. Vasya's questions: 1) >500? 2) <250? 3) >375? 4) <187? 5) >171? 7) >179? 8) <183? 9) >182? Answer: 183.

Send a comment