2002 AIME I Problems/Problem 9

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Problem

Harold, Tanya, and Ulysses paint a very long picket fence.

Harold starts with the first picket and paints every $h$ th picket;

Tanya starts with the second picket and paints every $t$ th picket; and

Ulysses starts with the third picket and paints every $u$ th picket.

Call the positive integer $100h+10t+u$ paintable when the triple $(h,t,u)$ of positive integers results in every picket being painted exaclty once. Find the sum of all the paintable integers.

Solution

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See also