Henry Ernest Dudeney/Modern Puzzles/184 - A Prohibition Poser/Solution 1
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Modern Puzzles by Henry Ernest Dudeney: $184$
- A Prohibition Poser
- The American Prohibition authorities discovered a full barrel of beer,
- and were about to destroy the liquor by letting it run down a drain
- when the owner pointed to two vessels standing by and begged to be allowed to retain in them a small quantity for the immediate consumption of his household.
- One vessel was a $7$-quart and the other a $5$-quart measure.
- The officer was a wag, and, believing it to be impossible, said that if the man could measure an exact quart into each vessel
- (without any pouring back into the barrel) he might do so.
- How was it to be done in the fewest possible transactions without any marking or other tricks?
- Pouring down the drain counts as one transaction.
- Perhaps I should state that an American barrel of beer contains exactly $120$ quarts.
Solution
Fill the $7$-quart measure and empty it down the drain a total of $14$ times.
Then you will have thrown away $98$ and have $22$ quarts left in the barrel.
This takes $28$ transactions.
Then perform the transactions according to the following:
- $\begin {array} {r|c|c|c} & \text {$7$-quart} & \text {$5$-quart} & \text {Barrel} \\ \hline
& 0 & 0 & 22 \\ (1): & 7 & 0 & 15 \\ (2): & 2 & 5 & 15 \\ (3): & 2 & 0 & 15 \\ (4): & 0 & 2 & 15 \\ (5): & 7 & 2 & 8 \\ (6): & 4 & 5 & 8 \\ (7): & 4 & 0 & 8 \\ (8): & 0 & 4 & 8 \\ (9): & 7 & 4 & 1 \\ (10): & 6 & 5 & 1 \\ (11): & 6 & 0 & 1 \\ (12): & 1 & 5 & 1 \\ (13): & 1 & 0 & 1 \\ (14): & 1 & 1 & 0 \\ \end {array}$
This is a total of $42$ transactions.
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $184$. -- A Prohibition Poser
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $404$. A Prohibition Poser