First of all, the fewest possible straight lines in each case are twenty-two, and in order that no cell may be visited twice it is absolutely necessary that each should pass into one cell and then immediately "visit" the one from which he started, afterwards proceeding by way of the second available cell. In the following diagram the man's route is indicated by the unbroken lines, and the lion's by the dotted lines. It will be found, if the two routes are followed cell by cell with two pencil points, that the lion and the man never meet. 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]