Henry Ernest Dudeney/Puzzles and Curious Problems/280 - The Ten Barrels/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $280$
- The Ten Barrels
- A merchant had ten barrels of sugar, which he placed in the form of a pyramid, as shown.
- Every barrel bore a different number, except one, which was not marked.
- It will be seen that he had accidentally arranged them so that the numbers in the three sides added up alike --
- that is, to $16$.
- Can you arrange them so that the three sides shall sum to the smallest number possible?
- Of course the central barrel (which happens to be $7$ in the diagram) does not come into the count.
Solution
The two basic solutions are as follows:
Changing the positions of the side numbers, while not changing the numbers contained on a side, gives another $8$ solutions in each case, not counting reflections or rotations as different.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $280$. -- The Ten Barrels
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $462$. The Ten Barrels