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)

I don't think there's anything wrong with using 10000 in the problem.  However, it does seem that it is going to require a computer-aided solution.  I have no problem with that, I think it takes a ton of talent to write a concise program that can solve problems like these, although I personally will be of no use finding the solution. :)

It would be interesting if a new problem could be created with sufficient restrictions such that the solution could be found by hand...

Posted by tomarken on 2006-03-21 08:58:35