The white squares on the chessboard represent the parishes of a diocese.  Place the bishop on any square you like, and so contrive that (using the ordinary bishop’s move of chess) he shall visit every one of his parishes in the fewest possible moves.  Of course, all the parishes passed through on any move are regarded as “visited.”  You can visit any squares more than once, but you are not allowed to move twice between the same two adjoining squares.  What are the fewest possible moves?  The bishop need not end his visitation at the parish from which he first set out.

326.—­A NEW COUNTER PUZZLE.

Here is a new puzzle with moving counters, or coins, that at first glance looks as if it must be absurdly simple.  But it will be found quite a little perplexity.  I give it in this place for a reason that I will explain when we come to the next puzzle.  Copy the simple diagram, enlarged, on a sheet of paper; then place two white counters on the points 1 and 2, and two red counters on 9 and 10, The puzzle is to make the red and white change places.  You may move the counters one at a time in any order you like, along the lines from point to point, with the only restriction that a red and a white counter may never stand at once on the same straight line.  Thus the first move can only be from 1 or 2 to 3, or from 9 or 10 to 7.

[Illustration: 

      4 8
     / \ / \
    2 6 10
     \ / \ /
      3 7
     / \ / \
    1 5 9

]

327.—­A NEW BISHOP’S PUZZLE.

[Illustration: 

+—–­+—–­+—–­+—–­+
| b | b | b | b |
+—–­+—–­+—–­+—–­+
|   |   |   |   |
+—–­+—–­+—–­+—–­+
|   |   |   |   |
+—–­+—–­+—–­+—–­+
| B | B | B | B |
+—–­+—–­+—–­+—–­+

]

This is quite a fascinating little puzzle.  Place eight bishops (four black and four white) on the reduced chessboard, as shown in the illustration.  The problem is to make the black bishops change places with the white ones, no bishop ever attacking another of the opposite colour.  They must move alternately—­first a white, then a black, then a white, and so on.  When you have succeeded in doing it at all, try to find the fewest possible moves.

If you leave out the bishops standing on black squares, and only play on the white squares, you will discover my last puzzle turned on its side.

328.—­THE QUEEN’S TOUR.

The puzzle of making a complete tour of the chessboard with the queen in the fewest possible moves (in which squares may be visited more than once) was first given by the late Sam Loyd in his Chess Strategy.  But the solution shown below is the one he gave in American Chess-Nuts in 1868.  I have recorded at least six different solutions in the minimum number of moves—­fourteen—­but this one is the best of all, for reasons I will explain.

[Illustration: