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Let $G$ be defined as the set of integers between 1 and .... Let $x$ be an integer in the set $G$, which defines the integer to be found. Then let integer $n$ represent the number of guesses required to find $x$. It then follows that the range of possible values for $n$ can be described such that $1 \leq n \leq \lceil \log_2 |G| \rceil \text{,}$ where the expression $\lceil \log_2 |G| \rceil$ gives the ceiling of the value given by the base-2 logarithm of the total number of elements within $G$ (i.e., $|G|$ indicates the size, or mode, of $G$). 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.