Henry Ernest Dudeney/Puzzles and Curious Problems/309 - Domino Sequences/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $309$
- Domino Sequences
- A boy who had a complete set of dominoes, up to double $9$, was trying to arrange them all in sequence, in the usual way --
- $6$ against $6$, $3$ against $3$, blank against blank, and so on.
- His father said to him, "You are attempting an impossibility, but if you let me pick out $4$ dominoes it can them be done.
- And those I take shall contain the smallest total number of pips possible in the circumstances.
- Now, which dominoes might the father have selected?
Solution
Remove from the set the four dominoes:
- $7 - 6$, $5 - 4$, $3 - 2$, $1 - 0$.
The remaining dominoes can be put together in proper sequence.
Any other combinations of these particular numbers will also do as well, for example:
- $7 - 0$, $6 - 1$, $5 - 2$, $4 - 3$
Generally, for any set of dominoes ending in a double odd number, those removed must contain together every number once from blank to two less than the highest number in the set.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $309$. -- Domino Sequences
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $488$. Domino Sequences