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?

This puzzle got posted so quickly I didn't get a chance to ask this question.  I needed an upper limit, but couldn't decide on 1000 or 10000.  Since I didn't get far with this myself before submitting it I just picked the more ambitious limit.  The chain found by Charlie is longer than I expected and it's very hard to see if it is optimal.  I won't propose this change, though.  It seems a bit late.  Maybe I'll submit the converse problem in a little while.

Posted by Jer on 2006-03-21 07:42:36