469. Groups of Dominoes. Is it known to any of my readers that if all 28 dominoes are laid out in a single line according to the usual rule (6 to 6, 2 to 2, blank to blank, etc.), the numbers at the ends will always match, so that the dominoes can actually be arranged in a circle? A very old trick involves hiding one of the dominoes (but don't take a double), and then asking someone to arrange the remaining dominoes in a line while you turn away. The audience is amazed when you, without looking at what has been done, name the numbers at the ends. These numbers match those on your hidden domino, since all the dominoes form a circle. If we arrange the dominoes as shown in the figure, and then break the chain into four pieces, each with 7 dominoes, it can be found that the sum of the points in the first group is 49, in the second 34, in the third 46, and in the fourth 39.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-168.jpg?height=663&width=763&top_left_y=1316&top_left_x=652)

I would like to arrange the dominoes into 4 groups such that the sums of the points in each group are equal. Can you do this?
469. The figure shows one of the solutions. The chain of dominoes is broken into 4 parts, each containing 7 pieces, and the sum of the points in each part is 22.

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-319.jpg?height=836&width=1102&top_left_y=530&top_left_x=480)