Question

Find which of the weights $1,3,9,27,81,.......$ lbs must be used to weigh ten thousand lbs, not more than one of each kind being used but in either scale that is necessary.

Answer 1

To represent ten thousand lbs in weights $1,3,9,27\cdot \cdot \cdot$ we need to convert $10,000$ in scale of three.

$10000=1\times 3^0+1\times 3^2+1\times 3^3+2\times 3^5+1\times 3^6+1\times 3^7+1\times 3^8$

Hence, we need:

$$\begin{array}{cc}Weights& Quantity\\ 1& 1\\ 3& 0\\ 9& 1\\ 27& 1\\ 81& 0\\ 243& 2\\ 729& 1\\ 2187& 1\\ 6561& 1\end{array}$$