Spoiler for New Scientist Enigma 1779 “Four triangles” (Follow the link to see the puzzle.)
Edited to correct two omissions, one pointed out by Jim Olson.
Is there an easier way to do this than to find or build a list of all Pythagorean triples with hypotenuse < 100 and start looking through it?
I find four chains of four if you allow the hypotenuse of each smaller triangle to be either leg of the next:
- 9-12-15 / 15-20-25 / 25-60-65 / 65-72-97
- 9-12-15 / 15-36-39 / 39-52-65 / 65-72-97
- 12-16-20 / 15-20-25 / 25-60-65 / 65-72-97
- 12-16-20 / 20-48-52 / 39-52-65 / 65-72-97
and the first two satisfy the requirement that the hypotenuse of the smaller triangle be the smaller leg of the next. In either case, the smallest and largest sides are 9 and 97.
Here’s a diagram of the second of these: