Competition problem — Combinatorics

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Combinatorics Difficulty 5.1 AIME, harder Find the answer

How many distinct sets of 8 positive odd integers sum to 20 ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

This is the same as the number of ways 8 nonnegative even integers sum to 12 (we subtract 1 from each integer in the above sum). All 11 possibilities are (leaving out 0s): $12,10+2,8+4,8+2+2,6+6,6+4+2,6+2+2+2+2,4+4+4,4+4+2+2$ , $4+2+2+2+2,2+2+2+2+2+2$ .

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Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.