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    This can be thought of as a fenceposting issue.

    That is, take some amount of s (try a few examples, like 21, 22, 40, 41, 42, 61 hint hint) and see how far you go.

    Even further, think about how, if you have gotten to square 42, you get to square 44, what is the next multiple of 42 you'll reach? How much strength is required to get there from 44 (what square will you actually end on whith that exact amount of strength?). Does a pattern emerge after that? Remember, this is a math problem; doing it iteratively is wasteful.