Henry Ernest Dudeney/Puzzles and Curious Problems/298 - The Stolen Balsam/Solution

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Puzzles and Curious Problems by Henry Ernest Dudeney: $298$

The Stolen Balsam
Three men robbed a gentleman of a vase containing $24$ ounces of balsam.
While running away, they met in the forest a glass seller, of whom, in a great hurry, they purchased three vessels.
On reaching a place of safety they wished to divide the booty,
but they found that their vessels contained $5$, $11$, and $13$ ounces respectively.
How could they divide the balsam into equal portions?


Solution

Solution $1$

One of several ways is as follows:

$\begin {array} {r|cccc}

& \mathrm {oz.} & \mathrm {oz.} & \mathrm {oz.} & \mathrm {oz.} \\ \hline \text {The vessels can hold} & 24 & 13 & 11 & 5 \\ \text {Their contents at the start} & 24 & 0 & 0 & 0 \\ \text {Make their contents} & 0 & 8 & 11 & 5 \\ \text {Then} & 16 & 8 & 0 & 0 \\ \text {Then} & 16 & 0 & 8 & 0 \\ \text {Then} & 3 & 13 & 8 & 0 \\ \text {Then} & 3 & 8 & 8 & 5 \\ \text {Then} & 8 & 8 & 8 & 0 \\ \end {array}$


Solution $2$

A solution using only $5$ transactions is as follows:

$\begin {array} {r|cccc}

& \mathrm {oz.} & \mathrm {oz.} & \mathrm {oz.} & \mathrm {oz.} \\ \hline \text {The vessels can hold} & 24 & 13 & 11 & 5 \\ \text {Their contents at the start} & 24 & 0 & 0 & 0 \\ \text {Make their contents} & 8 & 0 & 11 & 5 \\ \text {Then} & 8 & 11 & 0 & 5 \\ \text {Then} & 8 & 13 & 3 & 0 \\ \text {Then} & 8 & 8 & 3 & 5 \\ \text {Then} & 8 & 8 & 8 & 0 \\ \end {array}$


Historical Note

The $6$-transaction solution was the one provided by Dudeney.

The improved $5$-transaction solution was discovered by Victor Meally.


Sources

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