But there was one little point that ought not to be overlooked—­“they occasionally got glimpses of one another.”  Now, if we take one route for the man and merely reverse it for the lion, we invariably find that, going at the same speed, they never get a glimpse of one another.  But in our diagram it will be found that the man and the lion are in the cells marked A at the same moment, and may see one another through the open doorways; while the same happens when they are in the two cells marked B, the upper letters indicating the man and the lower the lion.  In the first case the lion goes straight for the man, while the man appears to attempt to get in the rear of the lion; in the second case it looks suspiciously like running away from one another!

[Illustration]

325.—­AN EPISCOPAL VISITATION.

[Illustration]

In the diagram I show how the bishop may be made to visit every one of his white parishes in seventeen moves.  It is obvious that we must start from one corner square and end at the one that is diagonally opposite to it.  The puzzle cannot be solved in fewer than seventeen moves.

326.—­A NEW COUNTER PUZZLE.

Play as follows:  2—­3, 9—­4, 10—­7, 3—­8, 4—­2, 7—­5, 8—­6, 5—­10, 6—­9, 2—­5, 1—­6, 6—­4, 5—­3, 10—­8, 4—­7, 3—­2, 8—­1, 7—­10.  The white counters have now changed places with the red ones, in eighteen moves, without breaking the conditions.

327.—­A NEW BISHOP’S PUZZLE.

[Illustration:  A]

[Illustration:  B]

Play as follows, using the notation indicated by the numbered squares in
Diagram A:—­

White.   |   Black.   |   White.    |    Black.
1. 18—­15  |  1. 3—­6   | 10. 20—­10  |  10. 1—­11
2. 17—­8   |  2. 4—­13  | 11. 3—­9    |  11. 18—­12
3. 19—­14  |  3. 2—­7   | 12. 10—­13  |  12. 11—­8
4. 15—­5   |  4. 6—­16  | 13. 19—­16  |  13. 2—­5
5. 8—­3    |  5. 13-18  | 14. 16—­1   |  14. 5—­20
6. 14—­9   |  6. 7—­12  | 15. 9—­6    |  15. 12—­15
7. 5—­10   |  7. 16-11  | 16. 13-7    |  16. 8—­14
8. 9—­19   |  8. 12—­2  | 17. 6—­3    |  17. 15-18
9. 10—­4   |  9. 11-17  | 18. 7—­2    |  18. 14—­19

Diagram B shows the position after the ninth move.  Bishops at 1 and 20 have not yet moved, but 2 and 19 have sallied forth and returned.  In the end, 1 and 19, 2 and 20, 3 and 17, and 4 and 18 will have exchanged places.  Note the position after the thirteenth move.

328.—­THE QUEEN’S TOUR.

[Illustration]

The annexed diagram shows a second way of performing the Queen’s Tour.  If you break the line at the point J and erase the shorter portion of that line, you will have the required path solution for any J square.  If you break the line at I, you will have a non-re-entrant solution starting from any I square.  And if you break the line at G, you will have a solution for any G square.  The Queen’s Tour previously given may be similarly broken at three different places, but I seized the opportunity of exhibiting a second tour.