perplexus.info :: Just Math : Watermelon weights

Watermelon weights (Posted on 2025-02-18)

Pete is preparing to sell watermelons on the farmer’s market next Saturday. He wants to prepare himself to be able to measure any integer weight from 1 to 120 pounds on his two-pan balance scales. How many masses must he prepare, at minimum?

No Solution Yet Submitted by Danish Ahmed Khan

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Five weights will do:

1 3 9 27 81

as 1 can be placed on the opposite pan from the 3 to effectively get 3-1=2. Then since you've got weights up to 4 you need a way to get 5 or more, which can be accomplished by 9-4=5 through 9+4=13. Then 14 through 40 can be obtained as 27-13 through 14+13, etc., where subtraction means placing weights on the opposite side.

Posted by Charlie on 2025-02-18 10:13:14

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