Problem of the Week 940

Determine the Weights

Suppose you are given two red balls, two blue balls, and two white balls, together with the information that one ball of each color has weight A and one ball of each color has weight B, with A not equal to B. Show how, using an equal-arm balance, you can learn all the weights of the balls in only two weighings.

Source: Ross Honsberger has written several informative problem books for the MAA. His latest, Mathematical Chestnuts from Around the World (published by the Math. Assoc. of America, 2001, www.maa.org), contains many problems at the level of the PoW program, and the present problem is taken from that book.

© Copyright 2001 Stan Wagon. Reproduced with permission.