Smallest Set of Weights for One-Pan Balance/Examples/63

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 $3$