Mixing
Minimum board size for knights tour to be possible
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What is the minimum board size for a knight's tour: open or closed, to be possible.
Edit: I want to write a program that can solve knight's tour for any board size. I want to implement a lower limit so that the program doesn't get stuck.
I also want to know if it is knight's tour is possible on unequal indexes i.e 7x8, 9x7
Added by Alex Ravsky. I think the question concerns a well-known (its history has more than a thousand years) and respected problem. The existence question is investigated and completely answered. So I vote to undelete and reopen this question and then to make it answered.
combinatorics graph-theory hamiltonian-path knight-tours
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
$endgroup$
add a comment |
$begingroup$
What is the minimum board size for a knight's tour: open or closed, to be possible.
Edit: I want to write a program that can solve knight's tour for any board size. I want to implement a lower limit so that the program doesn't get stuck.
I also want to know if it is knight's tour is possible on unequal indexes i.e 7x8, 9x7
Added by Alex Ravsky. I think the question concerns a well-known (its history has more than a thousand years) and respected problem. The existence question is investigated and completely answered. So I vote to undelete and reopen this question and then to make it answered.
combinatorics graph-theory hamiltonian-path knight-tours
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
$endgroup$
$begingroup$
1x1 or 0x0 seem like good candidates
$endgroup$
– Countingstuff
Dec 31 '17 at 9:34
$begingroup$
Not sure if you are trolling. For a knight to move, the minimum must be a 3x3 if the starting position is at a corner. I've read around and 5x5 seems to be minimum.
$endgroup$
– SlickToes192
Dec 31 '17 at 9:49
$begingroup$
In fact, for a square board and ruling out the cases $0$ and $1$, the minimum is $5$. A closed tour is possible if and only if the number is even.
$endgroup$
– Peter
Dec 31 '17 at 10:38
$begingroup$
A tour on a 3 X 7 board is possible. You might be interested in "Selected Papers on Fun and Games" by Donald E. Knuth.
$endgroup$
– awkward
Dec 31 '17 at 12:44
add a comment |
$begingroup$
What is the minimum board size for a knight's tour: open or closed, to be possible.
Edit: I want to write a program that can solve knight's tour for any board size. I want to implement a lower limit so that the program doesn't get stuck.
I also want to know if it is knight's tour is possible on unequal indexes i.e 7x8, 9x7
Added by Alex Ravsky. I think the question concerns a well-known (its history has more than a thousand years) and respected problem. The existence question is investigated and completely answered. So I vote to undelete and reopen this question and then to make it answered.
combinatorics graph-theory hamiltonian-path knight-tours
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
$endgroup$
What is the minimum board size for a knight's tour: open or closed, to be possible.
Edit: I want to write a program that can solve knight's tour for any board size. I want to implement a lower limit so that the program doesn't get stuck.
I also want to know if it is knight's tour is possible on unequal indexes i.e 7x8, 9x7
Added by Alex Ravsky. I think the question concerns a well-known (its history has more than a thousand years) and respected problem. The existence question is investigated and completely answered. So I vote to undelete and reopen this question and then to make it answered.
combinatorics graph-theory hamiltonian-path knight-tours
combinatorics graph-theory hamiltonian-path knight-tours
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
edited Jan 1 at 4:09
Alex Ravsky
41.1k32282
41.1k32282
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
asked Dec 31 '17 at 9:28
SlickToes192SlickToes192
62
62
$begingroup$
1x1 or 0x0 seem like good candidates
$endgroup$
– Countingstuff
Dec 31 '17 at 9:34
$begingroup$
Not sure if you are trolling. For a knight to move, the minimum must be a 3x3 if the starting position is at a corner. I've read around and 5x5 seems to be minimum.
$endgroup$
– SlickToes192
Dec 31 '17 at 9:49
$begingroup$
In fact, for a square board and ruling out the cases $0$ and $1$, the minimum is $5$. A closed tour is possible if and only if the number is even.
$endgroup$
– Peter
Dec 31 '17 at 10:38
$begingroup$
A tour on a 3 X 7 board is possible. You might be interested in "Selected Papers on Fun and Games" by Donald E. Knuth.
$endgroup$
– awkward
Dec 31 '17 at 12:44
add a comment |
$begingroup$
1x1 or 0x0 seem like good candidates
$endgroup$
– Countingstuff
Dec 31 '17 at 9:34
$begingroup$
Not sure if you are trolling. For a knight to move, the minimum must be a 3x3 if the starting position is at a corner. I've read around and 5x5 seems to be minimum.
$endgroup$
– SlickToes192
Dec 31 '17 at 9:49
$begingroup$
In fact, for a square board and ruling out the cases $0$ and $1$, the minimum is $5$. A closed tour is possible if and only if the number is even.
$endgroup$
– Peter
Dec 31 '17 at 10:38
$begingroup$
A tour on a 3 X 7 board is possible. You might be interested in "Selected Papers on Fun and Games" by Donald E. Knuth.
$endgroup$
– awkward
Dec 31 '17 at 12:44
$begingroup$
1x1 or 0x0 seem like good candidates
$endgroup$
– Countingstuff
Dec 31 '17 at 9:34
$begingroup$
1x1 or 0x0 seem like good candidates
$endgroup$
– Countingstuff
Dec 31 '17 at 9:34
$begingroup$
Not sure if you are trolling. For a knight to move, the minimum must be a 3x3 if the starting position is at a corner. I've read around and 5x5 seems to be minimum.
$endgroup$
– SlickToes192
Dec 31 '17 at 9:49
$begingroup$
Not sure if you are trolling. For a knight to move, the minimum must be a 3x3 if the starting position is at a corner. I've read around and 5x5 seems to be minimum.
$endgroup$
– SlickToes192
Dec 31 '17 at 9:49
$begingroup$
In fact, for a square board and ruling out the cases $0$ and $1$, the minimum is $5$. A closed tour is possible if and only if the number is even.
$endgroup$
– Peter
Dec 31 '17 at 10:38
$begingroup$
In fact, for a square board and ruling out the cases $0$ and $1$, the minimum is $5$. A closed tour is possible if and only if the number is even.
$endgroup$
– Peter
Dec 31 '17 at 10:38
$begingroup$
A tour on a 3 X 7 board is possible. You might be interested in "Selected Papers on Fun and Games" by Donald E. Knuth.
$endgroup$
– awkward
Dec 31 '17 at 12:44
$begingroup$
A tour on a 3 X 7 board is possible. You might be interested in "Selected Papers on Fun and Games" by Donald E. Knuth.
$endgroup$
– awkward
Dec 31 '17 at 12:44
add a comment |
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$begingroup$
1x1 or 0x0 seem like good candidates
$endgroup$
– Countingstuff
Dec 31 '17 at 9:34
$begingroup$
Not sure if you are trolling. For a knight to move, the minimum must be a 3x3 if the starting position is at a corner. I've read around and 5x5 seems to be minimum.
$endgroup$
– SlickToes192
Dec 31 '17 at 9:49
$begingroup$
In fact, for a square board and ruling out the cases $0$ and $1$, the minimum is $5$. A closed tour is possible if and only if the number is even.
$endgroup$
– Peter
Dec 31 '17 at 10:38
$begingroup$
A tour on a 3 X 7 board is possible. You might be interested in "Selected Papers on Fun and Games" by Donald E. Knuth.
$endgroup$
– awkward
Dec 31 '17 at 12:44