MathDB

An equilateral triangle side

10

is divided into

100

equilateral triangles of side

1

by lines parallel to its sides. There are m equilateral tiles of

4

unit triangles and

25 - m

straight tiles of

4

unit triangles (as shown below). For which values of

m

can they be used to tile the original triangle. [The straight tiles may be turned over.]

578