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AMO 2027 Grades 9-11 SET 4 - Self-study Question 4

AMO · AMO 2027 Grades 9-11 SET 4 - Self-study

Question 4

Find the set of ordered 4-tuples of positive integers $[w,x,y,z]$ such that $$w+x+y+z=21.$$

Editorial clarification: the source asks for the set, while its answer key gives a count. For the answer box, enter the number of such ordered tuples. The solution also describes the full set.

Enter one positive integer, without units.