Let $G$ be defined as the set of integers between 1 and ##. Let $x \in G$ be defined as the integer to be found. In a binary search, the set of possible answers is halved after each guess. Therefore, we can deduce the maximum number of required guesses: \[ 1 \leq x \leq \lceil \log_2 |G| \rceil \] In this case, we have a maximum of 0 possible guesses.

The binary search simulation below will use a pseudo-random number
generator to pick a number within the set $G$, after which the
algorithm runs until the target integer is found. The results will be
displayed, as well as a visual representation of eliminating incorrect
integers. Click the *simulate* link multiple times to run more
simulations. One interesting thing to note is that, once you begin
seeing integers being fully enumerated, the search has reduced the
possible number of answers below 100.