Briefly

The domino puzzle

The domino puzzle

I used to like dominoes a lot and I gave them to be an expert in the variant called muggins or decimal, until I met a certain Monsieur Blume in Paris, who showed me how little I knew about domino science.

Monsieur Blume was a professional player in his 80s who was born blind and earned a living by exhibiting his art in cafes and giving lessons to all his opponents.

I have always said that any game, such as cards or chess, can inspire us for a puzzle and in the process teach the key to the strategy of the game.

Monsieur Blume always finished the domino games as a riddle: he announced in advance that he would add five, ten or twenty points and always got it right. And that was what inspired this riddle:

What is the largest number of points that both players can make in a decimal domino in which the two extremes are counted whenever they add 5, 10, 15 or 20? ”

For those who do not have a domino on hand, the one in the illustration shows the 28 chips needed to solve the puzzle. Put one token each and count the ends.

In the decimal domino, it is scored whenever the sum of the extreme scores is a multiple of five. The game is started with a piece whose ends add up to a multiple of five (for example, card 2-3 that adds 5 to the game score, 5-5 that adds up to 10, etc.) and to score, form chips must be placed that the extremes add a multiple of 5. Thus, for example, if we have started with the 5-5 card, 10 points are added, if we now place the 5-0, 10 more points are added and so on until we place all the chips.

Solution

Patience and perseverance, combined with a small dose of good luck, will show a good domino player that, contrary to what is believed, 200 points can be made in a game of muggins or decimals. This problem occupied mathematicians for decades, setting the maximum limit at 195 points. But I discovered that 5 more points could be added.

The game admits variations but it would be basically like this: It starts with the 2-3 tab and the order of the chips would be as follows:

5-5, 5-6, 6-6, 6-2, 2-1, 1-1, 1-4, 4-2, 2-2, 2-3, 3-3, 3-1, 1-6, 6-4, 4-4, 4-3, 3-6, 6-0, 0-3, 3-5, 5-0, 0-0, 0-4, 4-5, 5-2, 2-0, 0-1, 1-5