For the test case [7 7 7] all of [1 7] [2 7] [3 7] should be valid responses, right? Also you don't have any test cases where the game is not winnable.
Extract leading non-zero digit
Recurring Cycle Length (Inspired by Project Euler Problem 26)
Reverse the elements of an array
Disjunctive Normal Form
Method of Common Differences part-1
Number of cyles and fixed points in a permutation
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