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?

The number of possibilities is more than I really I care to try to compute.  I did some code writing to limit the number of right triangles for consideration.  I've made the assumption that the right triangle to be attached to the chain can always be oriented so not to cause an overlap.  The right triangle had to have a pair of sides (no more, no less) that would match to other triangles to complete a chain.  The number I came up with is 225.  Adding 2 -- one for each end of the chain where only one side need match -- results in a total of 227.  My guess.

Posted by Dej Mar on 2006-03-21 19:15:37