Smallest Set of Weights for One-Pan Balance/Examples/63
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Examples of Smallest Set of Weights for One-Pan Balance
Consider a balance such that weights may be placed in one of the pans.
Let $S$ be the smallest set of weights needed to weigh any given integer weight up to $63$ units.
Then $\size S = 6$.
Proof
From Smallest Set of Weights for One-Pan Balance, a set of $6$ weights in the sequence $\sequence {2^n}$:
- $1, 2, 4, 8, 16, 32$
allows one to weigh any given integer weight up to $2^6 - 1 = 63$.
Hence the result.
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {1-2}$ The Basis Representation Theorem: Exercise $3$