The number of ways the king
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Let the king stand in the upper left corner on an 8x8 chessboard. How many options to get to the cell number $ (i,j), i,j in {1,2 ldots 8}$ if the king goes to each cell no more than once?
I do not know combinatorics very well, but I am very curious about the result. Sorry for not making any attempts.
p.s. it's not homework.
combinatorics discrete-mathematics
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
$endgroup$
|
show 1 more comment
$begingroup$
Let the king stand in the upper left corner on an 8x8 chessboard. How many options to get to the cell number $ (i,j), i,j in {1,2 ldots 8}$ if the king goes to each cell no more than once?
I do not know combinatorics very well, but I am very curious about the result. Sorry for not making any attempts.
p.s. it's not homework.
combinatorics discrete-mathematics
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
$endgroup$
$begingroup$
It’s easier to work out by for smaller boards. Try that, and then see if patterns emerge which you can generalize.
$endgroup$
– Zachary Hunter
Jan 6 at 7:12
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The king has to go to every square and can move diagonal, right?
$endgroup$
– WarreG
Jan 6 at 8:58
$begingroup$
yes, diagonal.....
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:43
$begingroup$
No more than one. Not for everyone
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:44
$begingroup$
So to clear things up, the king is allowed to move diagonal en needs to visit every cell once until it reaches the last cell (i,j)?
$endgroup$
– Belgium_Physics
Jan 6 at 9:57
|
show 1 more comment
$begingroup$
Let the king stand in the upper left corner on an 8x8 chessboard. How many options to get to the cell number $ (i,j), i,j in {1,2 ldots 8}$ if the king goes to each cell no more than once?
I do not know combinatorics very well, but I am very curious about the result. Sorry for not making any attempts.
p.s. it's not homework.
combinatorics discrete-mathematics
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
$endgroup$
Let the king stand in the upper left corner on an 8x8 chessboard. How many options to get to the cell number $ (i,j), i,j in {1,2 ldots 8}$ if the king goes to each cell no more than once?
I do not know combinatorics very well, but I am very curious about the result. Sorry for not making any attempts.
p.s. it's not homework.
combinatorics discrete-mathematics
combinatorics discrete-mathematics
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
asked Jan 6 at 7:09
Vladislav KharlamovVladislav Kharlamov
597216
597216
$begingroup$
It’s easier to work out by for smaller boards. Try that, and then see if patterns emerge which you can generalize.
$endgroup$
– Zachary Hunter
Jan 6 at 7:12
$begingroup$
The king has to go to every square and can move diagonal, right?
$endgroup$
– WarreG
Jan 6 at 8:58
$begingroup$
yes, diagonal.....
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:43
$begingroup$
No more than one. Not for everyone
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:44
$begingroup$
So to clear things up, the king is allowed to move diagonal en needs to visit every cell once until it reaches the last cell (i,j)?
$endgroup$
– Belgium_Physics
Jan 6 at 9:57
|
show 1 more comment
$begingroup$
It’s easier to work out by for smaller boards. Try that, and then see if patterns emerge which you can generalize.
$endgroup$
– Zachary Hunter
Jan 6 at 7:12
$begingroup$
The king has to go to every square and can move diagonal, right?
$endgroup$
– WarreG
Jan 6 at 8:58
$begingroup$
yes, diagonal.....
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:43
$begingroup$
No more than one. Not for everyone
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:44
$begingroup$
So to clear things up, the king is allowed to move diagonal en needs to visit every cell once until it reaches the last cell (i,j)?
$endgroup$
– Belgium_Physics
Jan 6 at 9:57
$begingroup$
It’s easier to work out by for smaller boards. Try that, and then see if patterns emerge which you can generalize.
$endgroup$
– Zachary Hunter
Jan 6 at 7:12
$begingroup$
It’s easier to work out by for smaller boards. Try that, and then see if patterns emerge which you can generalize.
$endgroup$
– Zachary Hunter
Jan 6 at 7:12
$begingroup$
The king has to go to every square and can move diagonal, right?
$endgroup$
– WarreG
Jan 6 at 8:58
$begingroup$
The king has to go to every square and can move diagonal, right?
$endgroup$
– WarreG
Jan 6 at 8:58
$begingroup$
yes, diagonal.....
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:43
$begingroup$
yes, diagonal.....
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:43
$begingroup$
No more than one. Not for everyone
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:44
$begingroup$
No more than one. Not for everyone
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:44
$begingroup$
So to clear things up, the king is allowed to move diagonal en needs to visit every cell once until it reaches the last cell (i,j)?
$endgroup$
– Belgium_Physics
Jan 6 at 9:57
$begingroup$
So to clear things up, the king is allowed to move diagonal en needs to visit every cell once until it reaches the last cell (i,j)?
$endgroup$
– Belgium_Physics
Jan 6 at 9:57
|
show 1 more comment
1 Answer
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This problem is generally in NP class of complexity and cannot be solved only through numerical analysis. Check out Self-avoiding walk
P.S. If it was a homework, it would have taken 2 or 3 month to solve it!
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
oldest
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$begingroup$
This problem is generally in NP class of complexity and cannot be solved only through numerical analysis. Check out Self-avoiding walk
P.S. If it was a homework, it would have taken 2 or 3 month to solve it!
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
$endgroup$
add a comment |
$begingroup$
This problem is generally in NP class of complexity and cannot be solved only through numerical analysis. Check out Self-avoiding walk
P.S. If it was a homework, it would have taken 2 or 3 month to solve it!
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
$endgroup$
add a comment |
$begingroup$
This problem is generally in NP class of complexity and cannot be solved only through numerical analysis. Check out Self-avoiding walk
P.S. If it was a homework, it would have taken 2 or 3 month to solve it!
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
$endgroup$
This problem is generally in NP class of complexity and cannot be solved only through numerical analysis. Check out Self-avoiding walk
P.S. If it was a homework, it would have taken 2 or 3 month to solve it!
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
answered Jan 6 at 7:55
Mostafa AyazMostafa Ayaz
15.6k3939
15.6k3939
add a comment |
add a comment |
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$begingroup$
It’s easier to work out by for smaller boards. Try that, and then see if patterns emerge which you can generalize.
$endgroup$
– Zachary Hunter
Jan 6 at 7:12
$begingroup$
The king has to go to every square and can move diagonal, right?
$endgroup$
– WarreG
Jan 6 at 8:58
$begingroup$
yes, diagonal.....
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:43
$begingroup$
No more than one. Not for everyone
$endgroup$
– Vladislav Kharlamov
Jan 6 at 9:44
$begingroup$
So to clear things up, the king is allowed to move diagonal en needs to visit every cell once until it reaches the last cell (i,j)?
$endgroup$
– Belgium_Physics
Jan 6 at 9:57