Charming little puzzle
I remembered this puzzle from an old Scientific American magazine last night. I think it's interesting because you can solve it fairly straightforwardly by either of the extremes of a purely logical approach, or the brute-force approach of trying all the possible combinations, but it's pretty diabolical if you approach it with trial and error or random playing. In that way it's a good puzzle to use to demonstrate the way a human brain best solves problems compared to how a stored-program computer does, and I kind of like that extra little gift.
The puzzle: In the figure below, place the digits 1 through 8 inside the circles such that consecutive digits are never in circles connected by a line. For example, if "4" is placed in the top circle, then neither "3" nor "5" can be placed in any of the three circles in the second row, because each of them is connected to the top circle. There is only one solution, not counting reflections.
Edit: solutions are being discussed in the comments; if you care to take an unspoiled crack at this yourself, don't look at them.