MathDB
Paintable

Source:

November 28, 2005
number theoryrelatively prime

Problem Statement

Harold, Tanya, and Ulysses paint a very long picket fence. Harold starts with the first picket and paints every hhth picket; Tanya starts with the second picket and paints everth ttth picket; and Ulysses starts with the third picket and paints every uuth picket. Call the positive integer 100h+10t+u100h+10t+u <spanclass=latexitalic>paintable</span><span class='latex-italic'>paintable</span> when the triple (h,t,u)(h,t,u) of positive integers results in every picket being painted exaclty once. Find the sum of all the paintable integers.