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 re(2): Solution, perhaps? by tomarken)

There will be several triangles that have a side that will be shared with more than one other triangle.  Simply finding the number of possible right triangles that have no side greater than 10000 is only half the battle.

Edited on March 20, 2006, 11:02 pm

Posted by Dej Mar on 2006-03-20 21:56:07