Find the minimum even number n, such that a square can be dissected into n triangles of equal area, with no two congruent.

Find the minimum odd n or prove impossible.

n=6 is possible.

Construct a 12*12 square with vertex A on the origin. The n=6 dissection can be achieved by marking points {4,4}, {2,8}, {0,4} and {0,8} then constructing the relevant triangles.  

By a theorem of Monsky, odd n do not produce any solutions, irrespective of the congruence of the triangles.

Edited on May 14, 2025, 6:56 am

Posted by broll on 2025-05-14 06:45:39