Written Q1: In the worst case, without any hints, a player could take 10 guesses to get the correct number since the player could went from 1 to 10 to guess the number if the correct number is 10 and the player start guessing from 1 then it would take 10 guesses.
Written Q2: If we will have hints for this question, it would take maximum 4 guesses to get the correct answer if we could eliminate half of the remaining numbers by picking the middle number of the sets. It can be represented as log base 2 of the number of remaining numbers. Since we have 10 numbers, the first guess could eliminate 5 numbers, log2(10) = 3.322, second guess would leave 2 or 3 numbers, log2(5) = 2.322, the third guess would leave 1 or 2 numbers remaining, log2(2) = 1, log2(3) = 1.585, and log2(1) = 0; such that, the fourth guess would gave us correct answer.
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