Triples Idea contributed by Grant Whitaker of Croftinloan School

Three numbers form a triple. No triple can include 0 or negative numbers. The smallest triple would make a sum of three i.e. (1, 1, 1)

How many triples are there with a sum of six?
(2,2,2), (2,1,3), (2,3,1), (3,2,1), (3,1,2), (4,1,1), (1,4,1), (1,1,4)
Eight triples with a sum of six? Are there any more? Are you sure? Check that I haven't missed any out.

How many triples are there with a sum of twenty?

Be systematic and draw up and ordered list. Make a table of your results. Look for a pattern.