Fig. 866.—Example 2.
Let us give this problem our attention for a few minutes, and we shall not find it difficult.
Take the first example. We will throw the cubes out of the box and put them back in the order shown in fig. 865.
We see now that 1 occupies the place of 11, 11 that of 7, 7 that of 8, 8 that of 6, 6 of 15, 15 of 1. This much is evident without any study. We formulate these figures as follows, beginning with 1 and working from figure to figure till we are led to 1 again, and so on.
1st. Series.—1, 11, 7, 8, 6, 15, 1 (6) even.
Counting the number of different cubes we have 6; and we put (6) in a parenthesis. We call the first series even because 6 is an even number.
We now establish, by the same formula, a second series commencing with 2, and going back to it, thus—
| 2nd Series.—2, 4, 2 | (2) even. |
| 3rd Series.—3, 5, 10, 12, 3 | (4) even. |
| 4th Series.—9, 13, 14, 9 | (3) uneven. |