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Math Prize 2010 Problem 12

Source:

November 14, 2010

Problem Statement

Say that an ordered triple (a,b,c)(a, b, c) is pleasing if
(a) aa, bb, and cc are in the set {1,2,…,17}\{ 1, 2, \dots, 17 \}, and
(b) both b−ab - a and c−bc - b are greater than 33, and at least one of them is equal to 44.
How many pleasing triples are there?
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