Henry Ernest Dudeney/Modern Puzzles/195 - Domino Groups

Modern Puzzles by Henry Ernest Dudeney: $195$

Domino Groups

I wonder how many of my readers know that if you lay out the $28$ dominoes in line according to the ordinary rules --

$6$ against $6$, $2$ against $2$, blank against blank, and so on --

the last number must always be the same as the first, so that they will really always form a circle.

It is a very ancient trick to conceal one domino (but do not take out a double) and then ask him to arrange all the others in line without your seeing.

It will astonish him when you tell him, after he has succeeded, what the two end numbers are.

They must be those on the domino that you have withdrawn, for that domino completes the circle.

If the dominoes are laid out in the manner shown in the diagram and I then break the line into $4$ lengths of $7$ dominoes each,

it will be found that the sum of the pips in the first group is $49$, in the second $34$, in the third $46$, and in the fourth $39$.

Now I want to play them out so that all the four groups of seven when the line is broken shall contain the same number of pips.

Can you find a way of doing it?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Problems Concerning Games: $195$. -- Domino Groups
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Domino Puzzles: $484$. Domino Groups