## Problem of the Week 1202## Magic TrianglesFind a 3×3 array of distinct positive integers so that: - the three numbers in each row, column, and two main diagonals form the edge lengths of a triangle; and
- the perimeters of the eight triangles that arise are all the same.
The idea is to minimize the sum of the nine entries. Here a "triangle" is a
"nondegenerate triangle": Unsolved problem: Same thing, but with "perimeter" replaced by "area." For this, consider only the rows and columns (not the diagonals; such is called a "semi-magic square"). Further, allow the entries to be any real numbers, but still aim for distinct entries (or possibly the weaker condition, that the triangles be distinct). Source: Lee Sallows, Nijmegen, The Netherlands. |

9 February 2015