Henry Ernest Dudeney/Puzzles and Curious Problems/305 - Domino Frames/Solution

by : $305$

 * Domino Frames

Solution

 * The three diagrams show a solution.


 * Dudeney-Puzzles-and-Curious-Problems-305-solution-1.png


 * Dudeney-Puzzles-and-Curious-Problems-305-solution-2.png


 * Dudeney-Puzzles-and-Curious-Problems-305-solution-3.png


 * The sum of all the pips is $132$.
 * One-third of this is $44$.
 * First divide the dominoes into any three groups of $44$ pips each.
 * Then, if we decide to try $12$ for the sum of the sides, $4$ times $12$ being $4$ more than $44$,
 * we must arrange in every case that the four corners in a frame shall sum to $4$.
 * The rest is done by trial and exchanges from one group to another of dominoes containing an equal number of pips.