I wrote a program for my calculator where the goal is for the user to determine the "randomly" selected number within a certain number of guesses. For the time being, I don't care that the number generator is only pseudorandom. The selected number, x, is always [itex] 1 \leq x \leq 100 [/itex], and the clues given are whether the number the user selects is closer, farther away, or the same distance from the selected number, compared to the previous guess. Basically, it's a hot and cold game. A sample of what the inputs and outputs might look like is as follows: ? 40 - Nope ? 60 - Hot ? 80 - Cold ? 51 - Hot ? 59 - Lukewarm ? 55 - Congratulations! You won! I have found a strategy that guarantees a win in no more than 10 guesses when on the 1-100 interval. Based on a limited number of small trials, I'm guessing that up to 2n+1, the optimum strategy will guarantee a win in no more than n+1 guesses. For the 1-100 interval, that means my guess is that no more than 8 guesses are needed for the optimum strategy. Can anyone here help me to verify that, and if possible, provide such a strategy?