Weighs and Means *** by Mike Shenk A Mathematical Logic Problem Professors Graham and Pound were just beginning their ex- antique balance from a corner of the tomb-the only weigh- cavation of King Itzunkhamen's tomb when they uncovered a ing instrument available to them-and a one-pound weight room containing 14 golden icons. from their bags, they made five weighings (as shown below) "I suggest we each take seven icons," said Graham. before the balance broke. "No, I believe it would be fairer if we each took the same Still, from the information gathered in these five weighings, total weight," argued Pound. At which point a prolonged de- the professors were able to solve their problem. Given that all bate began over the proper method of division. identical icons are also identical in weight, can you determine Several hours later it occurred to the two archeologists that (a) the actual weight of each icon, and (b) the correct perhaps both positions could be satisfied at once. Taking an division? Answer Drawer, page 66 The Icons 1. 2. 3. 5.4. If |v =11, w=23, and v-w=30, find v+w. Round your answer to one decimal place (if necessary). It is suggested that you include a diagram with your solution