How did he do that?!

This happened the other day while playing a board game.

Me: I was stumped by this question the other day. Do you think this is too hard for a high school student? Find values for p and q in which √p - √q = 5i.

Friend: *thinks for a few beats*
Well, that means I can choose whichever number, so I will choose 0 for q. Then all I need is for √p to equal 5i. That's easy, -25.

Me: *momentarily struck mute in a wide eyed stare*
Wow, that is amazing! You are absolutely right. But out of my 3 students, me, and my husband, only one of my students and you solved the problem that easily. We all ended up trying to solve it algebraically and didn't get anywhere. Kudos.

TL;DR (Too Long;Didn't Read) When the problem asks for any values that meet the requirement, the solution is as simple as choosing an easy to manage number. 

Have you ever been stuck on a problem and even asked others for help, only to solve it on your own later in an "aha eureka" moment?  If someone else solved the question quickly, how did that make you feel?