In the Mathworld article "Square Dissections" we find Guy (1989) asks if it is possible to triangulate a square with integer side lengths such that the resulting triangles have integer side lengths (Trott 2004, p. 104). There's more to this than I'm seeing right? If I interpret this to mean dissecting an square into integer-sided triangles, it doesn't seem very difficult. I can easily dissect a 12x12 square by tiling it with 3x4 rectangles and cutting the rectangles along random diagonals. I played with removing edges from those tilings and got a tiling of the 12x12 in 5 integer-sided triangles: 3-4-5, 5-5-6, 6-8-10, 10-10-12 and 9-12-15. But that solution dissection seems too simple that Guy would have overlooked it, so I'm thinking the original problem was more involved. So now the question is, can a square be dissected into fewer than 5 integer-sided triangles? 1 and 2 are clearly out. For 3, we cant use the square diagonal, so one of the triangles must have a square edge as a base and apex interior to the opposite side. I couldn't find integer solutions to this. For 4 triangles, I could not be sure I got all the possible configurations, but it might be an interesting investigation. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"