Question 5
A set of dominoes consists of the following 28 pieces:
The basic rule in playing dominoes is that, when two dominoes share a common edge, the numbers of dots inside the two squares which share that edge must be the same. The diagram shows an example of a hollow square formed from using all 28 domino pieces in accordance with the basic rule. The total number of dots along the lower side is 74, the total along the right side is 47 and the total along each of the other two sides is 59. The difference between the largest and the smallest totals is $74-47=27$.
Rearrange the domino pieces so that the difference between the largest and the smallest totals is as small as possible.
The basic rule in playing dominoes is that, when two dominoes share a common edge, the numbers of dots inside the two squares which share that edge must be the same. The diagram shows an example of a hollow square formed from using all 28 domino pieces in accordance with the basic rule. The total number of dots along the lower side is 74, the total along the right side is 47 and the total along each of the other two sides is 59. The difference between the largest and the smallest totals is $74-47=27$.
Rearrange the domino pieces so that the difference between the largest and the smallest totals is as small as possible.