A merchant has four weights: 1 lb, 3 lb, 9 lb, and 27 lb. Using a traditional two-pan balance scale, what is the heaviest whole-number weight in pounds that the merchant cannot weigh?
41
These powers of 3 can measure any weight from 1 up to the sum of all weights (1 + 3 + 9 + 27 = 40) by placing weights on either the same side as the item or the opposite side. Therefore, 40 is the maximum possible weight, making 41 the first weight that cannot be measured.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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