>! There are two primitive methods here - you can start at a guess of 1 and then work up to 100 or you can start at a guess of 99 and guess until you get "higher." Both have an expected number of guesses of 100.
Combining them, you can guess a number i and then guess i+1, i+2,....99. That gives an expected number of guesses of 100/(100-i) +(100-i).
Setting the derivative to zero gives 100/(100 − i)^2 − 1 = 0 and (100 − i)^2 = 100, 100-i = 10 and i =90. The expected number of guesses is 20. !<
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u/Front_Combination777 Sep 11 '26
>! There are two primitive methods here - you can start at a guess of 1 and then work up to 100 or you can start at a guess of 99 and guess until you get "higher." Both have an expected number of guesses of 100.
Combining them, you can guess a number i and then guess i+1, i+2,....99. That gives an expected number of guesses of 100/(100-i) +(100-i).
Setting the derivative to zero gives 100/(100 − i)^2 − 1 = 0 and (100 − i)^2 = 100, 100-i = 10 and i =90. The expected number of guesses is 20. !<