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Apply TodayA sequence of triangles is constructed in the following way:

1) the first triangle is Pythagoras' 3-4-5 triangle

2) the second triangle is a right-angle triangle whose second longest side is the hypotenuse of the first triangle, and whose shortest side is the same length as the second longest side of the first triangle

3) the third triangle is a right-angle triangle whose second longest side is the hypotenuse of the second triangle, and whose shortest side is the same length as the second longest side of the second triangle etc.

Each triangle in the sequence is constructed so that its second longest side is the hypotenuse of the previous triangle and its shortest side is the same length as the second longest side of the previous triangle.

What is the area of a square whose side is the hypotenuse of the nth triangle in the sequence?

512 correct solutions
479 incorrect solutions

Last solution submitted on Jul 20, 2016

26 players like this problem

1 Comment

Daniel Zimmermann
on 16 Jul 2016 at 14:06

Weak! My recursion solution should work just fine, but the server is unable to evaluate it properly. I'm going to count it.

1 Comment

Carlos Zúñiga
on 9 Mar 2016

Its the best way that I found :)

1 Comment

Raphael
on 20 Mar 2014

I consider my answer as a cheat

1 Comment

Jon
on 3 Feb 2014

yes, this is probably cheating

11 Comments