A NEW BISHOP'S PUZZLE.
(
The Guarded Chessboard)
[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.
Answer:
[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.
Informational
