The Triplet Puzzle


It's Halloween, and the triplets will be coming to my door, expecting candy. Ryan loves red candy (R), Giles loves green (G), and Bahara is a fan of blue (B).

I go to the store to get candy. The only R/G/B candies are Hurties (H), Marsh (M), and Nessy (N). Each company makes bags containing a particular number and color mixture as follows:

          Hurties      Marsh     Nessy
  # Red:     2           4        12
  # Green:   5           5         7
  # Blue:    6           7         3
  -------   --          --        --
  # Total:  13          16        22
I figure I want to give 100 pieces of candy to each of the triplets, and I really only want to give each triplet candies of their favorite color.

Is there a way to buy exactly 300 pieces of candy, which can be divided up by color to make each of the triplets happy? In other words, how many bags of H, M and N candy should I buy?

I give up, show me the solution.


Last revised on 27 January 2019.