Take a right triangle with integer sides A, B, & C.
(C need not be the hypotenuse.)

To side C attach another right triangle with integer sides C, D & E.

On this new triangle attach another right triangle to either side D or E.

Continue the process of attaching a new right triangle to the previous, creating a chain of integer right triangles.

No side length may be repeated.

If n is the number of triangles in the chain, what is the minimum largest side for n=2, 3, 4, 5, 6, 7, 8, 9, 10.

Well, I'm less certain for n = 7, but I think the minimum is 26.  Heres a 7 chain:

n =  7
-------
3-4-5
5-13-12
12-16-20
20-25-15
15-17-8
8-6-10
10-24-26

Posted by Steve Herman on 2006-06-17 08:14:36