Bertrand could see Allan's hat but not his own. Cecil could see Bertrand 's hat and Allan's hat, but not his own. After a minute nobody had solved the riddle. But then a short while later, one of them solved the riddle.
If a man goes to stand against the wall and all of the men already against the wall have the same color hat, then he just goes and stands at either end of the line. However, if a man goes to stand against the wall and there are men with both black and white hats already against the wall, he goes and stands between the two men with different colored ...
If Bertrand and Allan's hats were both the same color, then Cecil would know what color his hat was. But Cecil didn't know. So Bertrand knew that Allan's hat was a different color than his.
100 men are in a room, each wearing either a white or black hat. Nobody knows the color of his own hat, although everyone can see everyone else's hat. The men are not allowed to communicate with each other at all (and thus nobody will ever be able to figure out the color of his own hat).
You do not know the color of the hat on your own head. If one of you can guess the color of the hat on your head, I will let you free. But before you answer you must keep standing in this line. You cannot turn around. Here are my only hints: there are only black and white hats. At least one hat is black.