A merchant wants to weigh exactly 4 pounds of sugar using a 7-pound weight, a 9-pound weight, and a two-pan balance scale. What is the minimum number of weighings required?

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Place the 9-pound weight on one side of the scale and the 7-pound weight on the other side. The difference between 9 and 7 is 2 pounds. To balance them, you must pour 2 pounds of sugar onto the side with the 7-pound weight (7 + 2 = 9). Now, take those 2 pounds of sugar off the scale. Repeat this process once more: put the 9-pound weight and the 2 pounds of sugar on one side (total 11 lbs), and the 7-pound weight plus another 2 pounds of sugar on the other side (7 + 2 = 9... wait, that's two weighings). Actually, you can do it in 1 weighing if you put the 9-pound weight on the left pan, and the 7-pound weight plus the 4 pounds of sugar on the right pan? No, 7 + 4 = 11, which doesn't equal 9. Wait, can you put weights on *both* pans? Yes! Put the 9-pound weight on the left pan, and the 7-pound weight on the right pan. Then pour sugar into the right pan until it balances. That gives you 2 pounds of sugar in one go. To get 4 pounds, you simply do it a second time (or save those 2 pounds and weigh another 2 pounds). Thus, it takes 2 weighings, but wait—can you put the 9-pound weight on one side, and the 7-pound weight *plus* the 4 pounds of sugar on the other side? No. The minimum number of weighings is 2.