Finding a Pythagorean triple $a^2 + b^2 = c^2$ with $a+b+c=40$ Let's say you're asked to find a Pythagorean triple $a^2 + b^2 = c^2$ such that $a + b + c = 40$. The catch is that the question is asked at a job interview, and you weren't expecting questions about Pythagorean triples.
It is trivial to look up the answer. It is also trivial to write a computer program that would find the answer. There is also plenty of material written about the properties of Pythagorean triples and methods for generating them. However, none of this would be of any help during a job interview.
How would you solve this in an interview situation?

Here's a non-algebraic idea. Loosen your tie until you can remove it over your head. Then adjust it to 20 cm long when stretched out (ask the interview panel, politely, to provide a ruler) ie 40cm total loop length. Now form this into a right-angled triangle (ask for some help from the interview panel and use of their table - politely) and vary the legs until both are integer length (in cm). The hypotenuse must be integer (40  minus leg lengths) and being right-angled Pythagoras does the rest. My hunch is that this is the sort of approach they'd be after given the way the info. is provided ie a blend of background knowledge and practical application (based on many job interviews and enjoying 'watching the watchers' whilst going through the motions). 
