On a hot summer day, n equally bright philosophers, tired from all that philosophising, were napping in an orchard. A prankster came by, and painted all of their faces black with charcoal.

When the philosophers woke up, they started laughing at the others... until they suddenly realised all of their faces must be black!

How did they come to that conclusion?

Federico Kereki writes: "I think there's a mistake there. B should rather think: 'A has a white face, and so do I (I hope). C surely also thinks so... then how come C isn't surprised at seeing D laugh? What would he be laughing at? As A's face is white, the only possibility is that my own face is also black!' "

Bear with me, Mr. Kereki. Slowness of apprehension is just one of my many charms. B might think: "If my face is white, C is seeing two white faces, A's and mine, and one black face, D, and so he would conclude that his own face is black, and that is what D is laughing at. If my face is black, C would reason that D might be laughing at me. D would be reasoning the same way. So I don't know whether my face is white or black."