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Office Weighings - Solution

Puzzles -> Measuring Puzzles

 The Puzzle: You have a balance and the following items of which you know the weights: a small coin weighing 5g, a pen weighing 10g, an eraser weighing 20g, a holepunch weighing 40g, and a stapler weighing 80g.How many different possible weights can you measure with these items?

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The Solution . . .

 31.We could list all combinations, but noticing the doubling of each weight (5,10,20,40,80) we can see what happens as we introduce each weight (I include "0g" as a weighing on purpose):5g: can weigh 0g or 5g (2 possibilities)5g and 10g: can weigh 0g or 5g or 10g or 15g (4 possibilities)5g, 10g and 20g: can weigh 0g or 5g or 10g or 15g or 20g or 25g or 30g or 35g (8 possibilities)It doubles each time!So with 4 weights there are 16 possibilitiesAnd with 8 weights there are 32 possibilitiesIf you don't like "0g" as a weighing, just subtract one, for an answer of 31.

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