For a scholarship, at most n candidates out of 2n + 1 can be selected.
If the number of different ways of selection of at least one candidate
is 63, the maximum number of candidates that can be selected for
the scholarship is:

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This how I understand the question.
(2n+1) choose 1 + (2n+1) choose 2 +... +(2n+1) choose n = 63

solve for n?

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