Enigma1363.txt "Hat Stand" by Susan Denham, New Scientist, 22 October 2005, page 54. Knowledge (or lack of knowledge) begins at the back of the line and moves forward. The phrase "After a pause" that begins the 2nd paragraph implies that the person in back of the line sees 2 hats of each color, and therefore can't tell what color s/he's wearing. The next two persons (working from back to front) are Rene and Steve. They both can see two hats of the same color. Because the person in back couldn't see three hats of the same color, Rene and Steve know they're wearing a hat of the other color. The next person (that is, the second person from the front) is Quentin. He knows he must be wearing the same color hat as the person at the head of the line. Otherwise Rene and Steve couldn't have known the colors of their hats. Paul is either the person at the back of the line or in the front. We are told his hat is the same color as the one in the bag. He can't be the person in the back of the line; otherwise he would have seen three hats of the same color. He must be the person in front of the line. The order (from front to back assuming there's a White hat in the bag) is either: Paul Quentin Rene Steve Taina W W B B B or: Paul Quentin Steve Rene Taina W W B B B In both cases Rene can see a white hat. However, at the very beginning of the problem it is stated that Paul, Quentin, Rene, Steve, and Taina are "not in that order." It must be PQSRT.