Smallest Set of Weights for Two-Pan Balance/Examples/40

Examples of Smallest Set of Weights for Two-Pan Balance
Consider a set of balance scales such that weights may be placed in either or both of the pans. Let $S$ be the smallest set of weights needed to weigh any given integer weight up to $40$ units.

Then $\size S = 4$.

Proof
From Smallest Set of Weights for Two-Pan Balance, a set of $4$ weights in the sequence $\sequence {3^n}$:
 * $1, 3, 9, 27$

allows one to weigh any given integer weight up to $\dfrac {3^4 - 1} 2 = 40$.

Hence the result.