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

by : $182$

 * A New Domino Puzzle
 * 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.


 * Dudeney-Modern-Puzzles-182.png


 * 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.