My question is about the game of Hi-Lo which says that: A computer generates a number $X$ according to a known probability mass function $p(x), x ∈$ {$1, 2,..., 100$}. The player asks a question, “Is $X = i$?” and is told “Yes,” “You’re too high,” or “You’re too low.” He continues for a total of six questions. If he is right (i.e., he receives the answer “Yes”) during this sequence, he receives a prize of value $v(X)$. How should the player proceed to maximize his expected winnings?
Here in the solution, it says that the player cannot cover more than $63$ values of $X$ with $6$ questions. I want to know where does this $63$ comes from?