An excerpt from a likely-never-to-be-finished essay:

"Claude Shannon once told me that as a kid, he remembered being stuck on a jigsaw puzzle.

His brother, who was passing by, said to him: "You know: I could tell you something."

That's all his brother said.

Yet that was enough hint to help Claude solve the puzzle. The great thing about this hint... is that you can always give it to yourself."

--Manuel Blum, "Advice to a Beginning Graduate Student"