Every a can move from left to right one square at a time, and every b from right to left, and any piece can leap over one of another colour on to an unoccupied square. They can reverse their positions thus:—
If we number the cells or squares consecutively, and notice that at starting the vacant cell is No. 4, then in the successive moves the vacant cells will be 3, 5, 6, 4, 2, 1, 3, 5, 7, 6, 4, 2, 3, 5, 4. Of the moves thus indicated six are simple, and nine are leaps.
No. XXXVIII.—SORTING THE COUNTERS
The counters are changed in four moves only, moving two at a time as follows:—
| Move | 2 and 3 | to | 9 and 10. |
| „ | 5 and 6 | to | 2 and 3. |
| „ | 8 and 9 | to | 5 and 6. |
| „ | 1 and 2 | to | 8 and 9. |