Henry Ernest Dudeney/Puzzles and Curious Problems/301 - Weighing the Tea/Solution

by : $301$

 * Weighing the Tea

Solution
Having weighed a quantity of tea, we can then use that as a further weight to make further weighings.

We will refer to each weight merely by its numerical weight in pounds for simplicity.


 * $(1): \quad$ With the $5$-pound weight and the $9$-pound in opposite pans, weigh a $4$-pound weight of tea.


 * $(2): \quad$ With the $4$-pound weight of tea, weigh another $4$-pound weight of tea.


 * $(3): \quad$ With the $4$-pound weight of tea, weigh a third $4$-pound weight of tea.


 * $(4): \quad$ With the $4$-pound weight of tea, weigh a fourth $4$-pound weight of tea.
 * Note that the remaining tea in the chest will also make a $4$-pound weight of tea.


 * $(5)$ to $(9): \quad$ Divide each of the $4$-pound weights of tea equally between the two pans of the balance.