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

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