239 SOLUTIONS No problem is ever permanently closed. The editor is always pleased to consider for publication new solutions or new insightsonpastproblems.

Combination of solutionsby Gerry Leversha, St. Paul's School, London, England, and Kenneth M. Wilke, Topeka, KS, USA. Let n, b and c be the sides of the triangle. Since the perimeter n+ b+ c = 4n, if b < n then c > 2n, contradicting the triangle inequality. Hence we can take n < b < c < 2n. Furthermore we can assume that n, b and c are coprime; for, if (n; b) = d > 1 say, then djc since c = 3n b, and the triangle would be similar to a smaller triangle whose sides are coprime [and whose area is still an integer, since it is rational (A=d); by Heron's formula, any triangle with integer sides and semiperimeter and rational area has integer area. | Ed.]