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Swapping rooks in a 4x4 board
Swapping rooks in a 4x4 board
Rook game on chessboardThe Erasmus rook tourTwo rooks for Bobby FischerSwitch The KnightsFour free rooks for checkmateThe King's Routes Problem: How many possibilities?Interchanging Knights and RooksThe Minimized DropmateA Chess Lock Puzzle?Placing rooks on a chessboard
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
You have a 4x4 chessboard with four black rooks on the top and four white rooks in the bottom.
Your goal is to swap these rooks using the minimum number of steps. It does not matter which rook is which, as long as there are four white rooks on the top and four black rooks in the bottom.
Chess rules apply: rooks can move any number of squares, horizontally (left and right) or vertically (up and down), as long as there is not another piece on the way. White starts. You must alternate black and white moves.
chess optimization
asked 8 hours ago
ChaoticChaotic
661316
$endgroup$
add a comment |
$begingroup$
You have a 4x4 chessboard with four black rooks on the top and four white rooks in the bottom.
Your goal is to swap these rooks using the minimum number of steps. It does not matter which rook is which, as long as there are four white rooks on the top and four black rooks in the bottom.
Chess rules apply: rooks can move any number of squares, horizontally (left and right) or vertically (up and down), as long as there is not another piece on the way. White starts. You must alternate black and white moves.
chess optimization
asked 8 hours ago
ChaoticChaotic
661316
$endgroup$
1
$begingroup$
This is the type of question which might make a good secondary puzzle along the lines of "how many steps does it take to swap rooks on an nxn board"! (+1)
$endgroup$
– Adam
8 hours ago
1
$begingroup$
Yes, I thought about that. In a 3x3 board I was able to do in 14 moves, but I'm not sure if it is the optimal solution. I also don't think it would be a good idea to open a new question for a 3x3, 5x5, 8x8, etc.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
Not necessarily, but the generalization is a worthy question to ask, though perhaps not by itself not that you've asked the instance for n = 4. Still, I do believe this should generalize quite nicely.
$endgroup$
– greenturtle3141
6 hours ago
$begingroup$
I'm fairly sure that for a 3*3, 9 is optimal. Set up the rooks on the f-h files and ranks 1-3 and follow these moves: 1. Rh2 Rg2 2. Rgh3 Rg3 3. Rff2 Rhg1 4. Rh1 R1g2 5. Rg1 Rh2 6. Rfg2 Rff3 7. Rf2 Rhg2 8. Rhh1 Rh2 9. Rff1 Rhh3.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
It's white rooks on the first rank, black rooks on the third, and White to move first.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
$begingroup$
You have a 4x4 chessboard with four black rooks on the top and four white rooks in the bottom.
Your goal is to swap these rooks using the minimum number of steps. It does not matter which rook is which, as long as there are four white rooks on the top and four black rooks in the bottom.
Chess rules apply: rooks can move any number of squares, horizontally (left and right) or vertically (up and down), as long as there is not another piece on the way. White starts. You must alternate black and white moves.
chess optimization
asked 8 hours ago
ChaoticChaotic
661316
$endgroup$
You have a 4x4 chessboard with four black rooks on the top and four white rooks in the bottom.
Your goal is to swap these rooks using the minimum number of steps. It does not matter which rook is which, as long as there are four white rooks on the top and four black rooks in the bottom.
Chess rules apply: rooks can move any number of squares, horizontally (left and right) or vertically (up and down), as long as there is not another piece on the way. White starts. You must alternate black and white moves.
chess optimization
chess optimization
asked 8 hours ago
ChaoticChaotic
661316
asked 8 hours ago
ChaoticChaotic
661316
edited 8 hours ago
Chaotic
asked 8 hours ago
ChaoticChaotic
661316
asked 8 hours ago
ChaoticChaotic
661316
asked 8 hours ago
ChaoticChaotic
661316
661316
1
$begingroup$
This is the type of question which might make a good secondary puzzle along the lines of "how many steps does it take to swap rooks on an nxn board"! (+1)
$endgroup$
– Adam
8 hours ago
1
$begingroup$
Yes, I thought about that. In a 3x3 board I was able to do in 14 moves, but I'm not sure if it is the optimal solution. I also don't think it would be a good idea to open a new question for a 3x3, 5x5, 8x8, etc.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
Not necessarily, but the generalization is a worthy question to ask, though perhaps not by itself not that you've asked the instance for n = 4. Still, I do believe this should generalize quite nicely.
$endgroup$
– greenturtle3141
6 hours ago
$begingroup$
I'm fairly sure that for a 3*3, 9 is optimal. Set up the rooks on the f-h files and ranks 1-3 and follow these moves: 1. Rh2 Rg2 2. Rgh3 Rg3 3. Rff2 Rhg1 4. Rh1 R1g2 5. Rg1 Rh2 6. Rfg2 Rff3 7. Rf2 Rhg2 8. Rhh1 Rh2 9. Rff1 Rhh3.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
It's white rooks on the first rank, black rooks on the third, and White to move first.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
1
$begingroup$
This is the type of question which might make a good secondary puzzle along the lines of "how many steps does it take to swap rooks on an nxn board"! (+1)
$endgroup$
– Adam
8 hours ago
1
$begingroup$
Yes, I thought about that. In a 3x3 board I was able to do in 14 moves, but I'm not sure if it is the optimal solution. I also don't think it would be a good idea to open a new question for a 3x3, 5x5, 8x8, etc.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
Not necessarily, but the generalization is a worthy question to ask, though perhaps not by itself not that you've asked the instance for n = 4. Still, I do believe this should generalize quite nicely.
$endgroup$
– greenturtle3141
6 hours ago
$begingroup$
I'm fairly sure that for a 3*3, 9 is optimal. Set up the rooks on the f-h files and ranks 1-3 and follow these moves: 1. Rh2 Rg2 2. Rgh3 Rg3 3. Rff2 Rhg1 4. Rh1 R1g2 5. Rg1 Rh2 6. Rfg2 Rff3 7. Rf2 Rhg2 8. Rhh1 Rh2 9. Rff1 Rhh3.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
It's white rooks on the first rank, black rooks on the third, and White to move first.
$endgroup$
– Rewan Demontay
4 hours ago
1
1
$begingroup$
This is the type of question which might make a good secondary puzzle along the lines of "how many steps does it take to swap rooks on an nxn board"! (+1)
$endgroup$
– Adam
8 hours ago
$begingroup$
This is the type of question which might make a good secondary puzzle along the lines of "how many steps does it take to swap rooks on an nxn board"! (+1)
$endgroup$
– Adam
8 hours ago
1
1
$begingroup$
Yes, I thought about that. In a 3x3 board I was able to do in 14 moves, but I'm not sure if it is the optimal solution. I also don't think it would be a good idea to open a new question for a 3x3, 5x5, 8x8, etc.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
Yes, I thought about that. In a 3x3 board I was able to do in 14 moves, but I'm not sure if it is the optimal solution. I also don't think it would be a good idea to open a new question for a 3x3, 5x5, 8x8, etc.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
Not necessarily, but the generalization is a worthy question to ask, though perhaps not by itself not that you've asked the instance for n = 4. Still, I do believe this should generalize quite nicely.
$endgroup$
– greenturtle3141
6 hours ago
$begingroup$
Not necessarily, but the generalization is a worthy question to ask, though perhaps not by itself not that you've asked the instance for n = 4. Still, I do believe this should generalize quite nicely.
$endgroup$
– greenturtle3141
6 hours ago
$begingroup$
I'm fairly sure that for a 3*3, 9 is optimal. Set up the rooks on the f-h files and ranks 1-3 and follow these moves: 1. Rh2 Rg2 2. Rgh3 Rg3 3. Rff2 Rhg1 4. Rh1 R1g2 5. Rg1 Rh2 6. Rfg2 Rff3 7. Rf2 Rhg2 8. Rhh1 Rh2 9. Rff1 Rhh3.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
I'm fairly sure that for a 3*3, 9 is optimal. Set up the rooks on the f-h files and ranks 1-3 and follow these moves: 1. Rh2 Rg2 2. Rgh3 Rg3 3. Rff2 Rhg1 4. Rh1 R1g2 5. Rg1 Rh2 6. Rfg2 Rff3 7. Rf2 Rhg2 8. Rhh1 Rh2 9. Rff1 Rhh3.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
It's white rooks on the first rank, black rooks on the third, and White to move first.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
It's white rooks on the first rank, black rooks on the third, and White to move first.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
4 Answers
4
active
oldest
votes
$begingroup$
Got 19 by moving around... might be possible to do better:
1) a1-a3
2) d4-d2
3) b1-b3
4) d2-a2
5) d1-d4
6) a2-a1
7) c1-d1
8) c4-c1
9) b3-c3
10) b4-b1
11) a3-b3
12) a4-a2
13) d4-a4
14) a2-c2
15) d1-d4
16) c2-d2
17) b3-b4
18) d2-d1
19) c3-c4
answered 6 hours ago
shoopishoopi
572411
$endgroup$
add a comment |
$begingroup$
Found a solution in 20, though I have no idea if it's optimal. One of my assumptions was that "Chess rules apply" meant I had to alternate black and white moves.
answered 8 hours ago
TedTed
836
$endgroup$
$begingroup$
I have 2 that are different and 20 and I am not sure either.
$endgroup$
– Duck
8 hours ago
$begingroup$
Thanks, I've added the clarification.
$endgroup$
– Chaotic
8 hours ago
add a comment |
$begingroup$
Found a 19 move solution, but no idea about optimum.
a1-a3
a3-d3
b1-b2
b2-d2
a4-a1
b4-b1
c1-c2
c2-a2
a2-a4
c4-c1
d4-c4
c4-c3
d3-d4
d4-b4
d2-d4
d4-c4
d1-d4
c3-d3
d3-d1
Where the columns are a, b, c, d and rows are 1, 2, 3, 4, starting from bottom left.
answered 8 hours ago
SteveVSteveV
7,2182636
$endgroup$
1
$begingroup$
OP made an edit - moves must alternate between White and Black.
$endgroup$
– shoopi
7 hours ago
add a comment |
$begingroup$
EDIT: As @greenturtle pointed out in a comment, it seems that everyone else is doing the count by ply, and not the whole moves. The question is unclear to me about this on how the count is done. So thus my count is wrong by the majority's decision.
As such, just for fun, here is a symmetrical solution of 20 moves that uses the same notations as my below answer.
$1.$ Rh2 Rg3 $2.$ Rff2 Ree3 $3.$ Re2 Rh3 $4.$ Rg1 Rf4 $5.$ Rhf2 Reg3 $6.$ Rff1 Rgg4 $7.$ Ree1 Rhh4 $8.$ R4e2 R1h3 $9.$ Rh2 Re3 $10.$ Rhh1 Ree4
I found a solution in 12 moves. Here is a link to a GIF using Apronus. I'm using an 8 x 8 board for convenience in the gif, but I'm treating it as 4 x 4.
The following notation for my solution assumes that the files used are e through h and the ranks are 1 through 4, with the board being as it is from White's view on a normal chess board.
My Solution:
$1.$ Rg3 Rh2 $2.$ Rh3 Rhg2 $3.$ Rh4 Rg1 $4.$ R1h3 R4g2 $5.$ Rg3 Rh2 $6.$ Rgg4 Rhh1 $7.$ Re3 Rf2 $8.$ Rf3 Rfe2 $9.$ Rff4 Re1 $10.$ R1f3 R4e2 $11.$ Re3 Rf2 $12.$ Ree4 Rff1
I'm fairly sure that this is optimal due to how each rook moves a minimum of three times.
edited 1 hour ago
Duck
1,371117
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
$endgroup$
$begingroup$
Seems like the metric everyone else has adopted is total number of rook moves, in which case you'd have 24. I think people are reducing this to 20 by cleverly getting some rooks to the other side in one move.
$endgroup$
– greenturtle3141
4 hours ago
$begingroup$
Oh. Well than the question should speifcy that the count is in ply, not in whole moves as I thought.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
Your Answer
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Got 19 by moving around... might be possible to do better:
1) a1-a3
2) d4-d2
3) b1-b3
4) d2-a2
5) d1-d4
6) a2-a1
7) c1-d1
8) c4-c1
9) b3-c3
10) b4-b1
11) a3-b3
12) a4-a2
13) d4-a4
14) a2-c2
15) d1-d4
16) c2-d2
17) b3-b4
18) d2-d1
19) c3-c4
answered 6 hours ago
shoopishoopi
572411
$endgroup$
add a comment |
$begingroup$
Got 19 by moving around... might be possible to do better:
1) a1-a3
2) d4-d2
3) b1-b3
4) d2-a2
5) d1-d4
6) a2-a1
7) c1-d1
8) c4-c1
9) b3-c3
10) b4-b1
11) a3-b3
12) a4-a2
13) d4-a4
14) a2-c2
15) d1-d4
16) c2-d2
17) b3-b4
18) d2-d1
19) c3-c4
answered 6 hours ago
shoopishoopi
572411
$endgroup$
add a comment |
$begingroup$
Got 19 by moving around... might be possible to do better:
1) a1-a3
2) d4-d2
3) b1-b3
4) d2-a2
5) d1-d4
6) a2-a1
7) c1-d1
8) c4-c1
9) b3-c3
10) b4-b1
11) a3-b3
12) a4-a2
13) d4-a4
14) a2-c2
15) d1-d4
16) c2-d2
17) b3-b4
18) d2-d1
19) c3-c4
answered 6 hours ago
shoopishoopi
572411
$endgroup$
Got 19 by moving around... might be possible to do better:
1) a1-a3
2) d4-d2
3) b1-b3
4) d2-a2
5) d1-d4
6) a2-a1
7) c1-d1
8) c4-c1
9) b3-c3
10) b4-b1
11) a3-b3
12) a4-a2
13) d4-a4
14) a2-c2
15) d1-d4
16) c2-d2
17) b3-b4
18) d2-d1
19) c3-c4
answered 6 hours ago
shoopishoopi
572411
edited 6 hours ago
answered 6 hours ago
shoopishoopi
572411
answered 6 hours ago
shoopishoopi
572411
answered 6 hours ago
shoopishoopi
572411
572411
add a comment |
add a comment |
$begingroup$
Found a solution in 20, though I have no idea if it's optimal. One of my assumptions was that "Chess rules apply" meant I had to alternate black and white moves.
answered 8 hours ago
TedTed
836
$endgroup$
$begingroup$
I have 2 that are different and 20 and I am not sure either.
$endgroup$
– Duck
8 hours ago
$begingroup$
Thanks, I've added the clarification.
$endgroup$
– Chaotic
8 hours ago
add a comment |
$begingroup$
Found a solution in 20, though I have no idea if it's optimal. One of my assumptions was that "Chess rules apply" meant I had to alternate black and white moves.
answered 8 hours ago
TedTed
836
$endgroup$
$begingroup$
I have 2 that are different and 20 and I am not sure either.
$endgroup$
– Duck
8 hours ago
$begingroup$
Thanks, I've added the clarification.
$endgroup$
– Chaotic
8 hours ago
add a comment |
$begingroup$
Found a solution in 20, though I have no idea if it's optimal. One of my assumptions was that "Chess rules apply" meant I had to alternate black and white moves.
answered 8 hours ago
TedTed
836
$endgroup$
Found a solution in 20, though I have no idea if it's optimal. One of my assumptions was that "Chess rules apply" meant I had to alternate black and white moves.
answered 8 hours ago
TedTed
836
answered 8 hours ago
TedTed
836
answered 8 hours ago
TedTed
836
answered 8 hours ago
TedTed
836
836
$begingroup$
I have 2 that are different and 20 and I am not sure either.
$endgroup$
– Duck
8 hours ago
$begingroup$
Thanks, I've added the clarification.
$endgroup$
– Chaotic
8 hours ago
add a comment |
$begingroup$
I have 2 that are different and 20 and I am not sure either.
$endgroup$
– Duck
8 hours ago
$begingroup$
Thanks, I've added the clarification.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
I have 2 that are different and 20 and I am not sure either.
$endgroup$
– Duck
8 hours ago
$begingroup$
I have 2 that are different and 20 and I am not sure either.
$endgroup$
– Duck
8 hours ago
$begingroup$
Thanks, I've added the clarification.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
Thanks, I've added the clarification.
$endgroup$
– Chaotic
8 hours ago
add a comment |
$begingroup$
Found a 19 move solution, but no idea about optimum.
a1-a3
a3-d3
b1-b2
b2-d2
a4-a1
b4-b1
c1-c2
c2-a2
a2-a4
c4-c1
d4-c4
c4-c3
d3-d4
d4-b4
d2-d4
d4-c4
d1-d4
c3-d3
d3-d1
Where the columns are a, b, c, d and rows are 1, 2, 3, 4, starting from bottom left.
answered 8 hours ago
SteveVSteveV
7,2182636
$endgroup$
1
$begingroup$
OP made an edit - moves must alternate between White and Black.
$endgroup$
– shoopi
7 hours ago
add a comment |
$begingroup$
Found a 19 move solution, but no idea about optimum.
a1-a3
a3-d3
b1-b2
b2-d2
a4-a1
b4-b1
c1-c2
c2-a2
a2-a4
c4-c1
d4-c4
c4-c3
d3-d4
d4-b4
d2-d4
d4-c4
d1-d4
c3-d3
d3-d1
Where the columns are a, b, c, d and rows are 1, 2, 3, 4, starting from bottom left.
answered 8 hours ago
SteveVSteveV
7,2182636
$endgroup$
1
$begingroup$
OP made an edit - moves must alternate between White and Black.
$endgroup$
– shoopi
7 hours ago
add a comment |
$begingroup$
Found a 19 move solution, but no idea about optimum.
a1-a3
a3-d3
b1-b2
b2-d2
a4-a1
b4-b1
c1-c2
c2-a2
a2-a4
c4-c1
d4-c4
c4-c3
d3-d4
d4-b4
d2-d4
d4-c4
d1-d4
c3-d3
d3-d1
Where the columns are a, b, c, d and rows are 1, 2, 3, 4, starting from bottom left.
answered 8 hours ago
SteveVSteveV
7,2182636
$endgroup$
Found a 19 move solution, but no idea about optimum.
a1-a3
a3-d3
b1-b2
b2-d2
a4-a1
b4-b1
c1-c2
c2-a2
a2-a4
c4-c1
d4-c4
c4-c3
d3-d4
d4-b4
d2-d4
d4-c4
d1-d4
c3-d3
d3-d1
Where the columns are a, b, c, d and rows are 1, 2, 3, 4, starting from bottom left.
answered 8 hours ago
SteveVSteveV
7,2182636
answered 8 hours ago
SteveVSteveV
7,2182636
answered 8 hours ago
SteveVSteveV
7,2182636
answered 8 hours ago
SteveVSteveV
7,2182636
7,2182636
1
$begingroup$
OP made an edit - moves must alternate between White and Black.
$endgroup$
– shoopi
7 hours ago
add a comment |
1
$begingroup$
OP made an edit - moves must alternate between White and Black.
$endgroup$
– shoopi
7 hours ago
1
1
$begingroup$
OP made an edit - moves must alternate between White and Black.
$endgroup$
– shoopi
7 hours ago
$begingroup$
OP made an edit - moves must alternate between White and Black.
$endgroup$
– shoopi
7 hours ago
add a comment |
$begingroup$
EDIT: As @greenturtle pointed out in a comment, it seems that everyone else is doing the count by ply, and not the whole moves. The question is unclear to me about this on how the count is done. So thus my count is wrong by the majority's decision.
As such, just for fun, here is a symmetrical solution of 20 moves that uses the same notations as my below answer.
$1.$ Rh2 Rg3 $2.$ Rff2 Ree3 $3.$ Re2 Rh3 $4.$ Rg1 Rf4 $5.$ Rhf2 Reg3 $6.$ Rff1 Rgg4 $7.$ Ree1 Rhh4 $8.$ R4e2 R1h3 $9.$ Rh2 Re3 $10.$ Rhh1 Ree4
I found a solution in 12 moves. Here is a link to a GIF using Apronus. I'm using an 8 x 8 board for convenience in the gif, but I'm treating it as 4 x 4.
The following notation for my solution assumes that the files used are e through h and the ranks are 1 through 4, with the board being as it is from White's view on a normal chess board.
My Solution:
$1.$ Rg3 Rh2 $2.$ Rh3 Rhg2 $3.$ Rh4 Rg1 $4.$ R1h3 R4g2 $5.$ Rg3 Rh2 $6.$ Rgg4 Rhh1 $7.$ Re3 Rf2 $8.$ Rf3 Rfe2 $9.$ Rff4 Re1 $10.$ R1f3 R4e2 $11.$ Re3 Rf2 $12.$ Ree4 Rff1
I'm fairly sure that this is optimal due to how each rook moves a minimum of three times.
edited 1 hour ago
Duck
1,371117
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
$endgroup$
$begingroup$
Seems like the metric everyone else has adopted is total number of rook moves, in which case you'd have 24. I think people are reducing this to 20 by cleverly getting some rooks to the other side in one move.
$endgroup$
– greenturtle3141
4 hours ago
$begingroup$
Oh. Well than the question should speifcy that the count is in ply, not in whole moves as I thought.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
$begingroup$
EDIT: As @greenturtle pointed out in a comment, it seems that everyone else is doing the count by ply, and not the whole moves. The question is unclear to me about this on how the count is done. So thus my count is wrong by the majority's decision.
As such, just for fun, here is a symmetrical solution of 20 moves that uses the same notations as my below answer.
$1.$ Rh2 Rg3 $2.$ Rff2 Ree3 $3.$ Re2 Rh3 $4.$ Rg1 Rf4 $5.$ Rhf2 Reg3 $6.$ Rff1 Rgg4 $7.$ Ree1 Rhh4 $8.$ R4e2 R1h3 $9.$ Rh2 Re3 $10.$ Rhh1 Ree4
I found a solution in 12 moves. Here is a link to a GIF using Apronus. I'm using an 8 x 8 board for convenience in the gif, but I'm treating it as 4 x 4.
The following notation for my solution assumes that the files used are e through h and the ranks are 1 through 4, with the board being as it is from White's view on a normal chess board.
My Solution:
$1.$ Rg3 Rh2 $2.$ Rh3 Rhg2 $3.$ Rh4 Rg1 $4.$ R1h3 R4g2 $5.$ Rg3 Rh2 $6.$ Rgg4 Rhh1 $7.$ Re3 Rf2 $8.$ Rf3 Rfe2 $9.$ Rff4 Re1 $10.$ R1f3 R4e2 $11.$ Re3 Rf2 $12.$ Ree4 Rff1
I'm fairly sure that this is optimal due to how each rook moves a minimum of three times.
edited 1 hour ago
Duck
1,371117
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
$endgroup$
$begingroup$
Seems like the metric everyone else has adopted is total number of rook moves, in which case you'd have 24. I think people are reducing this to 20 by cleverly getting some rooks to the other side in one move.
$endgroup$
– greenturtle3141
4 hours ago
$begingroup$
Oh. Well than the question should speifcy that the count is in ply, not in whole moves as I thought.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
$begingroup$
EDIT: As @greenturtle pointed out in a comment, it seems that everyone else is doing the count by ply, and not the whole moves. The question is unclear to me about this on how the count is done. So thus my count is wrong by the majority's decision.
As such, just for fun, here is a symmetrical solution of 20 moves that uses the same notations as my below answer.
$1.$ Rh2 Rg3 $2.$ Rff2 Ree3 $3.$ Re2 Rh3 $4.$ Rg1 Rf4 $5.$ Rhf2 Reg3 $6.$ Rff1 Rgg4 $7.$ Ree1 Rhh4 $8.$ R4e2 R1h3 $9.$ Rh2 Re3 $10.$ Rhh1 Ree4
I found a solution in 12 moves. Here is a link to a GIF using Apronus. I'm using an 8 x 8 board for convenience in the gif, but I'm treating it as 4 x 4.
The following notation for my solution assumes that the files used are e through h and the ranks are 1 through 4, with the board being as it is from White's view on a normal chess board.
My Solution:
$1.$ Rg3 Rh2 $2.$ Rh3 Rhg2 $3.$ Rh4 Rg1 $4.$ R1h3 R4g2 $5.$ Rg3 Rh2 $6.$ Rgg4 Rhh1 $7.$ Re3 Rf2 $8.$ Rf3 Rfe2 $9.$ Rff4 Re1 $10.$ R1f3 R4e2 $11.$ Re3 Rf2 $12.$ Ree4 Rff1
I'm fairly sure that this is optimal due to how each rook moves a minimum of three times.
edited 1 hour ago
Duck
1,371117
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
$endgroup$
EDIT: As @greenturtle pointed out in a comment, it seems that everyone else is doing the count by ply, and not the whole moves. The question is unclear to me about this on how the count is done. So thus my count is wrong by the majority's decision.
As such, just for fun, here is a symmetrical solution of 20 moves that uses the same notations as my below answer.
$1.$ Rh2 Rg3 $2.$ Rff2 Ree3 $3.$ Re2 Rh3 $4.$ Rg1 Rf4 $5.$ Rhf2 Reg3 $6.$ Rff1 Rgg4 $7.$ Ree1 Rhh4 $8.$ R4e2 R1h3 $9.$ Rh2 Re3 $10.$ Rhh1 Ree4
I found a solution in 12 moves. Here is a link to a GIF using Apronus. I'm using an 8 x 8 board for convenience in the gif, but I'm treating it as 4 x 4.
The following notation for my solution assumes that the files used are e through h and the ranks are 1 through 4, with the board being as it is from White's view on a normal chess board.
My Solution:
$1.$ Rg3 Rh2 $2.$ Rh3 Rhg2 $3.$ Rh4 Rg1 $4.$ R1h3 R4g2 $5.$ Rg3 Rh2 $6.$ Rgg4 Rhh1 $7.$ Re3 Rf2 $8.$ Rf3 Rfe2 $9.$ Rff4 Re1 $10.$ R1f3 R4e2 $11.$ Re3 Rf2 $12.$ Ree4 Rff1
I'm fairly sure that this is optimal due to how each rook moves a minimum of three times.
edited 1 hour ago
Duck
1,371117
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
edited 1 hour ago
Duck
1,371117
edited 1 hour ago
Duck
1,371117
edited 1 hour ago
Duck
1,371117
1,371117
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
answered 5 hours ago
Rewan DemontayRewan Demontay
1,292221
1,292221
$begingroup$
Seems like the metric everyone else has adopted is total number of rook moves, in which case you'd have 24. I think people are reducing this to 20 by cleverly getting some rooks to the other side in one move.
$endgroup$
– greenturtle3141
4 hours ago
$begingroup$
Oh. Well than the question should speifcy that the count is in ply, not in whole moves as I thought.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
$begingroup$
Seems like the metric everyone else has adopted is total number of rook moves, in which case you'd have 24. I think people are reducing this to 20 by cleverly getting some rooks to the other side in one move.
$endgroup$
– greenturtle3141
4 hours ago
$begingroup$
Oh. Well than the question should speifcy that the count is in ply, not in whole moves as I thought.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
Seems like the metric everyone else has adopted is total number of rook moves, in which case you'd have 24. I think people are reducing this to 20 by cleverly getting some rooks to the other side in one move.
$endgroup$
– greenturtle3141
4 hours ago
$begingroup$
Seems like the metric everyone else has adopted is total number of rook moves, in which case you'd have 24. I think people are reducing this to 20 by cleverly getting some rooks to the other side in one move.
$endgroup$
– greenturtle3141
4 hours ago
$begingroup$
Oh. Well than the question should speifcy that the count is in ply, not in whole moves as I thought.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
Oh. Well than the question should speifcy that the count is in ply, not in whole moves as I thought.
$endgroup$
– Rewan Demontay
4 hours ago
add a comment |
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1
$begingroup$
This is the type of question which might make a good secondary puzzle along the lines of "how many steps does it take to swap rooks on an nxn board"! (+1)
$endgroup$
– Adam
8 hours ago
1
$begingroup$
Yes, I thought about that. In a 3x3 board I was able to do in 14 moves, but I'm not sure if it is the optimal solution. I also don't think it would be a good idea to open a new question for a 3x3, 5x5, 8x8, etc.
$endgroup$
– Chaotic
8 hours ago
$begingroup$
Not necessarily, but the generalization is a worthy question to ask, though perhaps not by itself not that you've asked the instance for n = 4. Still, I do believe this should generalize quite nicely.
$endgroup$
– greenturtle3141
6 hours ago
$begingroup$
I'm fairly sure that for a 3*3, 9 is optimal. Set up the rooks on the f-h files and ranks 1-3 and follow these moves: 1. Rh2 Rg2 2. Rgh3 Rg3 3. Rff2 Rhg1 4. Rh1 R1g2 5. Rg1 Rh2 6. Rfg2 Rff3 7. Rf2 Rhg2 8. Rhh1 Rh2 9. Rff1 Rhh3.
$endgroup$
– Rewan Demontay
4 hours ago
$begingroup$
It's white rooks on the first rank, black rooks on the third, and White to move first.
$endgroup$
– Rewan Demontay
4 hours ago