Henry Ernest Dudeney/Modern Puzzles/185 - Prohibition Again/Solution
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Modern Puzzles by Henry Ernest Dudeney: $185$
- Prohibition Again
- Let us now try to discover the fewest possible manipulations under the same conditions as in the last puzzle,
- except that we may now pour back into the barrel.
- The last puzzle
- 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
Perform the transactions according to the following:
- $\begin {array} {r|c|c|c} & \text {$7$-quart} & \text {$5$-quart} & \text {Barrel} \\ \hline
& 0 & 0 & 120 \\ (1): & 7 & 0 & 113 \\ (2): & 7 & 5 & 108 \\ (2): & 7 & 5 & 0 \\ (4): & 7 & 0 & 5 \\ (5): & 2 & 5 & 5 \\ (6): & 2 & 0 & 10 \\ (7): & 0 & 2 & 10 \\ (8): & 7 & 2 & 3 \\ (9): & 4 & 5 & 3 \\ (10): & 4 & 0 & 8 \\ (11): & 0 & 4 & 8 \\ (12): & 7 & 4 & 1 \\ (13): & 6 & 5 & 1 \\ (14): & 6 & 0 & 1 \\ (15): & 1 & 5 & 1 \\ (16): & 1 & 0 & 1 \\ (17): & 1 & 1 & 0 \\ \end {array}$
This is a total of $17$ transactions.
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $185$. -- Prohibition Again
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $405$. Prohibition Again