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# Measuring Kilograms - Solution

Puzzles -> Measuring Puzzles

 The Puzzle: In front of you is a balance. Can you devise a system, using only 4 weights, that can measure any whole number of kilograms (1,2,3, etc) …a) ... up to 15 kg ?b) ... up to 40 kg ?c) ... up to 80 kg ?

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## The Solution . . .

 a) Up to 15 kg: Weights are: 1 kg, 2 kg, 4 kg, 8 kgLike this:1 kg = 1 kg2 kg = 2 kg3 kg = 2 kg + 1 kg...14 kg = 8 kg + 4kg + 2 kg15 kg = 8 kg + 4 kg + 2 kg + 1 kgb) Up to 40 kg:Weights are: 1 kg, 3 kg, 9 kg, 27 kgLike this:You can put the weights on the other side of the balance, therefore subtracting some of the weight from the other side. Using this system the objects can be weighed thus:1kg = 1kg2kg = 3kg - 1kg3kg = 3kg...39kg = 27kg + 9kg + 3kg40kg = 27kg + 9kg + 3kg + 1kgc) Up to 80 kg:Weights are: 2 kg, 6 kg, 18 kg, 54 kgLike this:Put 2kg on one side, your item on the other. If item is less then 2kg, it is 1 kg. If it is more, put 6kg on one side, your item and 2kg on the other. If item and 2kg are less then 6kg, item is 3kg. If it is more, put 6kg on one side, your item on the other. If item is less then 6kg, it's 5kg....etc, up to 80 kg

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