2025 HMMT November General Round Problem 2

Suppose n integers are placed in a circle such that each of the following conditions is satisfied:

- at least one of the integers is 0; - each pair of adjacent integers differs by exactly 1; and - the sum of the integers is exactly 24.

Compute the smallest value of n for which this is possible.

Answers are checked by value, so any equivalent form is accepted: 1/2, \frac{1}{2} and 0.5 all count as the same answer.

Full credit goes to HMMT for authoring these problems. This problem is from the November 2025 contest; the official solution is available on the HMMT archive. HMMT is not affiliated with or endorsing TopsOJ in any way.