Suppose you have a two pan balance and gram weights, one for each power of three: 1 3, 9, 27, ... . Given a weight, say 21 grams, you can measure it by putting the 27 and 3 on one pan and the 9 on the other. So 21 = 27(1) + 9(-1) + 3(1) + 1(0)
The sequence of multipliers {1, -1, 1, 0} is the balanced ternery representation of 21. In general, a balance ternery representation is a sequence {a_{n},...a_{2},a_{1},a_{0}} where each a_{j} is -1,0, or 1; and the value of a_{j} is interpreted as follows:
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