Square / Eq. Triangle Dissection Problems

Antreas P. Hatzipolakis xpolakis at otenet.gr
Fri May 28 23:06:41 CEST 1999

The following problem appeared in the Monthly, but I don't know of
any published solutions:

Let n be fixed. In how many ways can a square be dissected into
(a) n congruent rectangles
(b) n rectangles of equal area?
     AMM 88(1981) 444 (E 2894) proposed by Thomas Ihringer

I posted the same problem, but for Equilateral Triangle, to sci.math
(under the pseudonym Radamanthys) but there were no responses:
In how many ways can an Eq. Tr. be dissected into n triangles of equal area?

I found by hand (a computer program would be of great help!):

n   ways
1    1
2    3
3    16
4    100 (?)

Does anyone know of any sequences related to these problems?


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