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This algorithm fails in the case that the duplicated number appears more than twice in the list, which is explicitly allowed by the problem statement.

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It’s not, on Leetcode. I submitted it as an answer and it worked. In the case where the number is repeated more than once (m times), you have an array of n+m elements. Divide the sum by m, subtract, problem solved.

In that case, their test suite doesn’t cover all relevant cases. Consider nums = [1,1,1,1,4]: There are 5 elements, so n=4, and all elements are within the range [1,4]; only the 1 is duplicated. This fulfills all of the listed requirements.

The actual sum is 8, and the 4th triangular number is 10, so the duplicated number according to your algorithm must be -2 (or some fraction thereof, depending on how you calculate m).

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