Mathematical_Recreations-Kraitchik-2e

Permutational Problems
eter give 2n - 1 arrangements satisfying the requirements
of the headmistress.
Another method of solution uses an arrangement such as
that shown in Figure 106. (Here also we take n = 6.) Twelve
lettered cubes fit easily into a box, forming two rows as
FIGURE 105.
shown. A vertical fin between the two rows keeps the rows
separated, except at the ends. The pairs in the vertical columns
of the given figure form the arrangement for one day.
To find another, remove the cube marked L, slip A into its
FIGURE 106.
place, slide the rest of the cubes in the top row to the left,
move G up to the top row, slide the lower row to the right,
and replace L. The vertical pairs give the new arrangement.
Successive arrangements are found by repeating this procedure,
always removing L and sliding the other cubes around
in tbe counterclockwise direction before replacing L.
2. ROUND DANCES. Children are dancing in a circle.
Can successive arrangements be determined by which each