Henry Ernest Dudeney/Modern Puzzles/182 - A New Domino Puzzle

Modern Puzzles by Henry Ernest Dudeney: $182$

Two dominoes have been placed together so that by taking the pips in unbroken conjunction

I can get all the numbers from $1$ to $9$ inclusive.

Thus, $1$, $2$ and $3$ can be taken alone;

then $1$ and $3$ make $4$; $3$ and $2$ make $5$; $3$ and $3$ make $6$;

$1$, $3$ and $3$ make $7$; $3$, $3$ and $2$ make $8$, and $1$, $3$, $3$ and $2$ make $9$.

It would not have been allowed to take the $1$ and the $2$ to make $3$, nor to take the first $3$ and the $2$ to make $5$.

The numbers would not have been in conjunction.

Now try to arrange four dominoes so that you can make the pips in this way sum to any number from $1$ to $24$ inclusive.

The dominoes need not be placed $1$ against $1$, $2$ against $2$, and so on, as in play.

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Measuring, Weighing, and Packing Puzzles: $182$. -- A New Domino Puzzle
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Domino Puzzles: $481$. A New Domino Puzzle