Outwitting the Weighing Machine - Solution

Puzzles -> Sam Loyd Puzzles

The Puzzle: The five school children in couples weigh 129 pounds, 125 pounds, 124 pounds, 123 pounds, 122 pounds, 121 pounds, 120 pound, 118 pounds, 116 pounds and 114 pounds on a weighing machine. What was the weight of each one of the five little girls if taken separately?

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The Solution . . .

It can readily be shown that there could be just ten different combination couples weighed, and that their separate weights must have been 56, 58, 60, 64, and 65 pounds to produce weights as given of 129, 125, 124, 123, 122, 121 120, 118, 116 and 114, and as we find by comparison of the weights of the third weight with the lightest and the second, that the lightest is two pounds lighter, we know that she weighs 156 and the next 158, after which it is easy to tell the rest.

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