4
votes
3answers
184 views

Dissecting an equilateral triangle into equilateral triangles of pairwise different sizes

It is know that a square can be dissected into other square such that no two of the squares have the same size. This is the simplest dissection of that kind: Is it also possible to dissect an ...
27
votes
1answer
1k views

Dividing a square into equal-area rectangles

How many ways are there to tile an $n\times n$ square with exactly $n$ rectangles, each of which has integer sides and area $n$? The sequence $C(n)$ begins 1, 2, 2, 9, 2, 46, 2, 250, 37. Clearly ...