2026 AMC 8 Problem 18
Attempt Problem 18 of the 2026 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2026 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
In how many ways can be written as the sum of two or more consecutive odd positive integers that are arranged in increasing order?
Answer: B
Small hint:
Write the terms as
Big hint:
Their sum is , so must divide
Video solution:
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Written solution:
Suppose there are terms, starting with odd positive integer . The sum is . Testing divisors of , the positive odd starts occur for , giving , and for , giving . Thus there are ways.
Problem 18 in other years
- 1985 AMC 8
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