A cognitive psychologist I worked with referred to these as insight problems. You need to have one critical piece of insight to solve the problem, and then it'

A cognitive psychologist I worked with referred to these as insight problems. You need to have one critical piece of insight to solve the problem, and then it's done. If you have the insight, you solve it, if you don't, you don't. He was constantly bemoaning how much of the research into human thinking revolved around insight problems, which you can give each subject once and at best time how long it takes for the insight to occur, instead of repeatable cognitive tasks that you could give the same subjects over and over while varying different parameters, to draw richer conclusions from.