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 remember seeing a proof of the following statement:

"For any right triangle with sides of integer length, the length of at least one of the sides must be a multiple of five (5)."

Just looking at my initial doodling for this problem, this bit of information seems to limit the number of possible triangles significantly.

Posted by Rollercoaster on 2006-03-20 14:35:54