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money to guess no from 1 to 144 - All-Russian MO 1998 Regional (R4) 10.8

Source:

September 17, 2024
combinatoricsnumber theory

Problem Statement

A number from 11 to 144144 is guessed. You are allowed to select a subset of the set of numbers from 1 1 to 144144 and ask whether the guessed number belongs to it. For the answer “yes” you have to pay 22 rubles, for the answer “no” - 11 ruble. What is the smallest amount of money needed to surely guess that?
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