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 Solution, perhaps? by J. Lindert)

Since no side may have length over 10000 and each triangle adds 2 sides, you could have at most, even on a naive basis, 4999 triangles, as the first triangle uses 3 sides.

Posted by Charlie on 2006-03-20 13:18:58