This completes the schedule. It will be found on examination that every number is between every pair of the other numbers once, and once only.
In order to reduce our first-day ring to exact numerical order we have only to interchange the numbers 4 and 5 throughout. The first three lines for example would then become:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| 1 | 3 | 5 | 6 | 4 | 7 | 8 | 2 | |
| 1 | 5 | 4 | 7 | 6 | 8 | 2 | 3, | etc. |
or, by putting letters for figures,
| A | B | C | D | E | F | G | H | |
| A | C | E | F | D | G | H | B | |
| A | E | D | G | F | H | B | C, | etc. |
An arrangement of the guests is thus arrived at for twenty-one successive days, so that not one of them has the same two neighbours on any two occasions.
No. XCIII.—MAKING MANY SQUARES
Can you apply the two oblongs drawn below to the two concentric squares, so as to produce thirty-one perfect squares?
