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 integer right triangles.

No side length may be repeated.

If n is the number of triangles in the chain, what is the minimum largest side for n=2, 3, 4, 5, 6, 7, 8, 9, 10.

I believe the following may be solutions for n=8, 9, and 10.

3- 4- 5
5-13-12
12-16-20
20-25-15
15-17- 8   N  MIN
8- 6-10    6   25
10-26-24   7   26
24-18-30   8   30

3- 4- 5
5-13-12
12-37-35
35-28-21
21-29-20
20-15-25
25- 7-24
24-26-10   N  MIN
10- 6- 8   9   37

3- 4- 5
5-13-12
12-37-35
35-28-21
21-29-20
20-15-25
25- 7-24
24-18-30
30-50-40   N  MIN
40-41- 9  10   50

Posted by Dej Mar on 2006-06-19 05:51:17