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 right triangles.

Three further rules:
1. No side length may be repeated.
2. No triangles may overlap.
3. No side may have length over 10000.

How many triangles can you make in this chain?

I think the possible number would be infinite, since you can have an infinite amount of lengths. If you have z(n) different lengths, the difference between z(y) and z(y + 1) would be x, where lim (x -> 0).

PS. In z(n), n is the index.

Posted by J. Lindert on 2006-03-20 12:49:59