Martha the grocer has a 2-pan scale and a set of 4 brass weights. She claims that she can weigh out any whole number of ounces up to 40 ounces using just these weights, and she’s right. What is the weight of each brass weight? (Note that you can put weights on either pan of the scale, so both adding and subtracting are possible.)
The weights are 1, 3, 9, and 27 ounces. Here’s how you can weigh 1 – 40 ounces on a 2-pan scale:
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1 = 1 2 + 1 = 3 3 = 3 4 = 1 + 3 5 + 1 + 3 = 9 6 + 3 = 9 11 + 1 = 3 + 9 16 +3 + 9 = 1 + 27 |
21 + 9 = 3 + 27 22 + 9 = 1 + 3 + 27 23 + 1 + 3 = 27 24 + 3 = 27 25 + 3 = 1 + 27 26 + 1 = 27 31 = 1 + 3 + 27 36 = 9 + 27 |