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AMO 2027 Grades 10-12 SET 1 - Self-study Question 1

AMO · AMO 2027 Grades 10-12 SET 1 - Self-study

Question 1

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

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

Enter one whole number, without units.