Swapping Knights and Bishops
Place a white knight and a white bishop at locations 1 and 3 of the
4x5 chessboard shown. Place a black knight and a black bishop at
locations 17 and 19.
4x5 board
+--+--+--+--+--+
|WK| 5| 9|13|BK|
+--+--+--+--+--+
| 2| 6|10|14|18|
+--+--+--+--+--+
|WB| 7|11|15|BB|
+--+--+--+--+--+
| 4| 8|12|16|20|
+--+--+--+--+--+
|
Starting from this position,
- Swap the positions of the white knight and white bishop.
- Swap the colors (swap the positions of the two knights and
the two bishops.)
At no time may any piece be under attack by a piece of the opposite
color. Moves do not need to alternate in color.
|
Source: Original. Similar to
Puzzle of July 20, 1998.
I'd be interested if this could be made more difficult, perhaps by
placing four pieces on each side.
Solutions were received from Philippe Fondanaiche
and Paul Botham.
UPDATE 9/20/2004: Richard Mathar found the following solutions:
9 moves for number 1.
1 WB 3-6
|WK| | | |BK|
| |WB| | | |
| | | | |BB|
| | | | | |
2 BB 19-14
|WK| | | |BK|
| |WB| |BB| |
| | | | | |
| | | | | |
3 WB 6-16
|WK| | | |BK|
| | | |BB| |
| | | | | |
| | | |WB| |
4 BK 17-15
|WK| | | | |
| | | |BB| |
| | | |BK| |
| | | |WB| |
5 WK 1-10
| | | | | |
| | |WK|BB| |
| | | |BK| |
| | | |WB| |
6 WK 10-3
| | | | | |
| | | |BB| |
|WK| | |BK| |
| | | |WB| |
7 WB 16-1
|WB| | | | |
| | | |BB| |
|WK| | |BK| |
| | | | | |
8 BK 15-17
|WB| | | |BK|
| | | |BB| |
|WK| | | | |
| | | | | |
9 BB 14-19
|WB| | | |BK|
| | | | | |
|WK| | | |BB|
| | | | | |
18 moves for number 2:
18 moves:
0:
|WK| | | |BK|
| | | | | |
|WB| | | |BB|
| | | | | |
1:
| | | | |BK|
| | | | | |
|WB|WK| | |BB|
| | | | | |
2:
| | | | |BK|
| |WB| | | |
| |WK| | |BB|
| | | | | |
3:
| | | | | |
| |WB|BK| | |
| |WK| | |BB|
| | | | | |
4:
| | | | | |
| | |BK| | |
| |WK|WB| |BB|
| | | | | |
5:
| | | | | |
| | | | | |
|BK|WK|WB| |BB|
| | | | | |
6:
|WK| | | | |
| | | | | |
|BK| |WB| |BB|
| | | | | |
7:
|WK| | | | |
| | | | | |
| | |WB| |BB|
| | |BK| | |
8:
|WK| |BB| | |
| | | | | |
| | |WB| | |
| | |BK| | |
9:
| | |BB| | |
| | |WK| | |
| | |WB| | |
| | |BK| | |
10:
| | |BB| |WK|
| | | | | |
| | |WB| | |
| | |BK| | |
11:
| | | | |WK|
| | | | | |
|BB| |WB| | |
| | |BK| | |
12:
| | | | |WK|
| | | | | |
|BB| |WB| |BK|
| | | | | |
13:
| | | | | |
| | | | | |
|BB| |WB|WK|BK|
| | | | | |
14:
| | | | | |
| | |BK| | |
|BB| |WB|WK| |
| | | | | |
15:
| | | | | |
| | |BK|WB| |
|BB| | |WK| |
| | | | | |
16:
|BK| | | | |
| | | |WB| |
|BB| | |WK| |
| | | | | |
17:
|BK| | | | |
| | | | | |
|BB| | |WK|WB|
| | | | | |
18:
|BK| | | |WK|
| | | | | |
|BB| | | |WB|
| | | | | |
(Original solutions) I don't if Philippe's solutions are optimum.
Anyone care to say they are or find shorter?
Philippe's solutions:
a) swap the positions of the white knight and white bishop
1 BB 19-14
2 BK 17-15
3 WK 1-10
4 BB 14-11
5 WK 10-19
6 WK 19-12
7 BK 15-17
8 WB 3-9
9 BB 11-8
10 WB 9-6
11 WB 6-1
12 BK 17-15
13 BB 8-17
14 WK 12-3
b) and swap the positions of the black knight and black bishop
15 BK 15-8
16 WK 3-5
17 WB 1-6
18 BK 8-10
19 BK 10-19
20 WB 6-1
21 WK 5-3
c) swap the colors
the first nine moves are the same as in a)
10 BK 17-10
11 BK 10-1
12 WB 9-19
13 WK 12-6
14 WK 6-13
15 BB 8-3
16 WK 13-11
17 WK 11-2
18 BB 3-6
19 WK 2-8
20 BK 1-7
21 WK 8-10
22 WK 10-17
23 BB 6-3
24 BK 7-1
Very probably the number of moves should be improved in all the 3 cases....
Paul's solutions:
Swapping Knights and Bishops
Swap the positions of the white knight and white bishop
13-11,19-14,1-10,14-11,10-19,19-12,15-17,
3-9,12-3,9-19,17-15,11-17,19-16,16-1,17-14,
15-17,14-19
[17 moves - KD]
Swap the colors
13-11,19-14,1-10,14-11,10-19,19-12,15-17,
3-9,12-3,9-19,17-15,11-17,19-16,16-1,17-14,
3-7,15-9,9-2,14-9,10-17,9-3,1-16,2-9,16-11,
9-7,17-15,11-17,7-1,17-14,15-17,14-19
[31 moves - KD]
Mail to Ken