Think of the operations that a weigh scale can do, that is +, -, and zero or balance. What mathematics principle does this remind you of? What pattern does it imply?
The scale is the principle of additive inverses. The range is in powers of 3.
Geometrically this is is a unit circle on the number line at zero (balance). The range of weights with a weight of one is two +-(-1)= 2. Fold this over at 1 and you get the next circle at three, which is the value of your next weight. Repeat, the range for 3-(-3)=6 fold over at three and you get 9, the value of your next weight. Repeat, the range for 9-(-9)=18 fold over at nine and you get 27, the value of your next weight. 1+3+9+27=40 and you have all the digits covered from 1 to forty.
Image is a numberline with circles about the origin with radius 1, 3, 9, and 27 and it can keep going.
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