MathDB
How can we make products?

Source: 1981 National High School Mathematics League, Problem 10

February 20, 2020

Problem Statement

To make three kinds of products A,B,CA,B,C, we have three parts a,b,ca,b,c. A product AA is made of twoaa and two bb; a product BB is made of one bb and one cc; a product CC is made of two aa and one cc. We have a few parts. If we make pp productAA, qq productBB, rr productCC, then 22 part aa and 11 part bb are remained. Prove: no matter how we make products, we cannot use up all the parts.