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?

(In reply to Is 10000 too big? by Jer)

We can be fairly sure that the chain I found via computer was not the longest, as the program crashed while still increasing the length of the chain. Plus, it was still investigating only one start of the chain; it had not the time to backtrack and try other branches.

Posted by Charlie on 2006-03-21 08:57:20