Henry Ernest Dudeney/Puzzles and Curious Problems/310 - Two Domino Squares/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $310$
- Two Domino Squares
- Arrange the $28$ dominoes as shown in the diagram to form two squares
- so that the pips in every one of the eight sides shall add up alike.
- The constant addition must of course be within limits to make the puzzle possible,
- and it will be interesting to find those limits.
- Of course, the dominoes need not be laid according to the rule, $6$ against $6$, blank against blank, and so on.
Solution
This solution has $22$ as the constant sum.
- With $22$ as this constant sum, the corners must add to $8$,
- with $23$ to $16$, with $24$ to $24$, with $25$ to $32$, with $26$ to $40$.
- The constant sum cannot be less than $22$ or more than $26$.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $310$. -- Two Domino Squares
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $489$. Two Domino Squares