Smallest Set of Weights for Two-Pan Balance/Mistake

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$31$

Mistake

Using both pans, the solution is similar, but now relies on expressing the weight as the sum and difference of powers of $3$. With the weights $1$, $3$, $9$ and $27$ it is possible to weight up to $40$. In general the weights up to $3$ will weigh up to a maximum of $\frac 1 2 \paren {3^{n + 1} - 1}$.

Correction

In that last sentence there is a typo.

It should say:

... the weights up to $3^n$ will weigh ...

This typo does not exist in the first edition of David Wells: Curious and Interesting Numbers.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $31$