Tessellate S.T.E.M.S (2019) - Mathematics - Category B - Set 3 - Objective Problem 5
Alex and Ben are playing a game in which Alex thinks of a number in the set and Ben has to guess the number. If Ben guesses correctly, Ben wins. Otherwise, at each incorrect guess of Ben, Alex increases or decreases his number by one, keeping the number in the set.
What is the minimum number such that Ben has a strategy to win the game within moves?
This problem is a part of Tessellate S.T.E.M.S. (2019) .
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1 solution
Guessing 2 , 3 , 4 , 5 , 5 , 4 , 3 , 2 is a winning strategy. The first four moves will win whenever Alex started with an even number, and the last four will win whenever Alex started with an odd number (by symmetry).
I am not sure how to prove that this strategy is optimal. The good news is that it generalizes to larger sets: on { 1 , 2 , … , N } , Ben can win in 2 N − 4 moves with the same strategy: 2 , 3 , 4 , … , N − 1 , N − 1 , … , 4 , 3 , 2 .