Reverse Puzzling

George is a great puzzler, so I was extremely surprised when he didn't immediately know the answer to a really famous puzzle. It's a puzzle that you probably did years ago, and have heard so often you can do it from memory rather than working it out. It's also not really that difficult, so I was also surprised when it appeared to be stumping him.

"Come on, surely you know this one." I said.

"I don't. And don't call me Shirley." He answered grumpily. I could tell his mood was declining rapidly, but like any great puzzler he was down and not out, and I watched his facial expression change as he reached into his mental bag of tricks. He nodded towards a conveniently located white board. "Have you got a marker for that?"

I handed him one, and he drew up the following diagram:

He stepped back, admiring his work, beaming proudly. "Well, now the solution is very obvious!" he commented. And indeed it was. The question for you is:

What is the puzzle?

Solution

The diagram represents the puzzle about the man, trying to cross the river with a fox (F), a chicken (C) and a sack of barley (B). He can carry at most one of them with himselves in the boat, and he shouldn't leave the chicken alone with the fox or with the barley on one side of the river. The red dots represent all admissable configurations and the lines between them all available moves.