Henry Ernest Dudeney/Puzzles and Curious Problems/353 - The Three Sugar Basins/Solution

by : $353$

 * The Three Sugar Basins

Solution

 * $36$

Proof
Let $n$ be the number of lumps each basin contains before starting.

Each sugar bowl transfers a total of $9 \times \dfrac n {18} = \dfrac n 2$ lumps to the teacups.

So after this transaction, each sugar bowl contains $n - \dfrac n 2 = \dfrac n 2$ lumps.

Each teacup then contains a total of $3 \times \dfrac n {18} = \dfrac n 6$ lumps.

Hence:
 * $\dfrac n 2 = \dfrac n 6 + 12$

which after algebra leads us to:
 * $n = 36$