Henry Ernest Dudeney/Puzzles and Curious Problems/280 - The Ten Barrels/Solution

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:

$\qquad$

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