On the latest episode of Scam School, Brian Brushwood presented three old brain teasers. Here's my favorite.
Make a five-by-five grid of dots. Then draw a cross by connecting the dots in such a way that five dots are enclosed by the cross and eight dots are outside the cross. The example on the right satisfies the first part (five dots inside the cross) but it fails the second requirement (it has four dots outside, but needs eight.)
You can learn the solution by watching the video.