Finding the average distance between all points [on hold]
-2
$begingroup$
We have a board whose size is $ N times N $. Let $ D $ be the taxicab distance between two squares on the board i.e. the distance a rook from chess would take to move. What is the floor of the average value of $ D $? What if instead we use the Chebyshev distance i.e. the distance a king would take to move?
I have no idea how to start even, or where I should search for a clue. (besides brute-force of course). I tried already with randomly picking two points $ N^2 $ times, but the approximation is too big.
mathematics chess
edited 5 hours ago
PiIsNot3
1,56321
asked 5 hours ago
Pitcher_21Pitcher_21
11
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by Glorfindel, noedne, Brandon_J, Rubio♦ 3 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Glorfindel, noedne, Brandon_J, Rubio
If this question can be reworded to fit the rules in the help center, please edit the question.
|
show 2 more comments
-2
$begingroup$
We have a board whose size is $ N times N $. Let $ D $ be the taxicab distance between two squares on the board i.e. the distance a rook from chess would take to move. What is the floor of the average value of $ D $? What if instead we use the Chebyshev distance i.e. the distance a king would take to move?
I have no idea how to start even, or where I should search for a clue. (besides brute-force of course). I tried already with randomly picking two points $ N^2 $ times, but the approximation is too big.
mathematics chess
edited 5 hours ago
PiIsNot3
1,56321
asked 5 hours ago
Pitcher_21Pitcher_21
11
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
put on hold as off-topic by Glorfindel, noedne, Brandon_J, Rubio♦ 3 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Glorfindel, noedne, Brandon_J, Rubio
If this question can be reworded to fit the rules in the help center, please edit the question.
2
$begingroup$
Is this a question that comes from somewhere else, or one you've made up?
$endgroup$
– Gareth McCaughan♦
5 hours ago
$begingroup$
Isn't Manhattan distance the minimum number of moves for (not a rook, but) a piece that moves like a rook but only one square at a time? Or, equivalently, like a king but not diagonally.
$endgroup$
– Gareth McCaughan♦
5 hours ago
3
$begingroup$
Hi @Pitcher_21, welcome to Puzzling SE! Like Gareth commented, this appears to be a problem you got from some other source other than yourself. If it is, can you include the source in your question? Thanks!
$endgroup$
– PiIsNot3
5 hours ago
1
$begingroup$
Note that taxicab distance is simply the sum of the distances on each dimension, so you can treat each independently. In fact, you can double the value you get from simply considering the one dimensional case. That should make this problem trivial IMO.
$endgroup$
– Don Thousand
4 hours ago
1
$begingroup$
This post from MSE applies here. If your lecturer gave you this question, (s)he must think that you should be able to gain something by trying it yourself. Having other people do it for you will gain you nothing at all.
$endgroup$
– Arnaud Mortier
2 hours ago
|
show 2 more comments
-2
-2
-2
$begingroup$
We have a board whose size is $ N times N $. Let $ D $ be the taxicab distance between two squares on the board i.e. the distance a rook from chess would take to move. What is the floor of the average value of $ D $? What if instead we use the Chebyshev distance i.e. the distance a king would take to move?
I have no idea how to start even, or where I should search for a clue. (besides brute-force of course). I tried already with randomly picking two points $ N^2 $ times, but the approximation is too big.
mathematics chess
edited 5 hours ago
PiIsNot3
1,56321
asked 5 hours ago
Pitcher_21Pitcher_21
11
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
We have a board whose size is $ N times N $. Let $ D $ be the taxicab distance between two squares on the board i.e. the distance a rook from chess would take to move. What is the floor of the average value of $ D $? What if instead we use the Chebyshev distance i.e. the distance a king would take to move?
I have no idea how to start even, or where I should search for a clue. (besides brute-force of course). I tried already with randomly picking two points $ N^2 $ times, but the approximation is too big.
mathematics chess
mathematics chess
edited 5 hours ago
PiIsNot3
1,56321
asked 5 hours ago
Pitcher_21Pitcher_21
11
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 5 hours ago
PiIsNot3
1,56321
asked 5 hours ago
Pitcher_21Pitcher_21
11
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 5 hours ago
PiIsNot3
1,56321
edited 5 hours ago
PiIsNot3
1,56321
edited 5 hours ago
PiIsNot3
1,56321
1,56321
asked 5 hours ago
Pitcher_21Pitcher_21
11
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Pitcher_21Pitcher_21
11
asked 5 hours ago
Pitcher_21Pitcher_21
11
11
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Pitcher_21 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Glorfindel, noedne, Brandon_J, Rubio♦ 3 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Glorfindel, noedne, Brandon_J, Rubio
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Glorfindel, noedne, Brandon_J, Rubio♦ 3 hours ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – Glorfindel, noedne, Brandon_J, Rubio
If this question can be reworded to fit the rules in the help center, please edit the question.
2
$begingroup$
Is this a question that comes from somewhere else, or one you've made up?
$endgroup$
– Gareth McCaughan♦
5 hours ago
$begingroup$
Isn't Manhattan distance the minimum number of moves for (not a rook, but) a piece that moves like a rook but only one square at a time? Or, equivalently, like a king but not diagonally.
$endgroup$
– Gareth McCaughan♦
5 hours ago
3
$begingroup$
Hi @Pitcher_21, welcome to Puzzling SE! Like Gareth commented, this appears to be a problem you got from some other source other than yourself. If it is, can you include the source in your question? Thanks!
$endgroup$
– PiIsNot3
5 hours ago
1
$begingroup$
Note that taxicab distance is simply the sum of the distances on each dimension, so you can treat each independently. In fact, you can double the value you get from simply considering the one dimensional case. That should make this problem trivial IMO.
$endgroup$
– Don Thousand
4 hours ago
1
$begingroup$
This post from MSE applies here. If your lecturer gave you this question, (s)he must think that you should be able to gain something by trying it yourself. Having other people do it for you will gain you nothing at all.
$endgroup$
– Arnaud Mortier
2 hours ago
|
show 2 more comments
2
$begingroup$
Is this a question that comes from somewhere else, or one you've made up?
$endgroup$
– Gareth McCaughan♦
5 hours ago
$begingroup$
Isn't Manhattan distance the minimum number of moves for (not a rook, but) a piece that moves like a rook but only one square at a time? Or, equivalently, like a king but not diagonally.
$endgroup$
– Gareth McCaughan♦
5 hours ago
3
$begingroup$
Hi @Pitcher_21, welcome to Puzzling SE! Like Gareth commented, this appears to be a problem you got from some other source other than yourself. If it is, can you include the source in your question? Thanks!
$endgroup$
– PiIsNot3
5 hours ago
1
$begingroup$
Note that taxicab distance is simply the sum of the distances on each dimension, so you can treat each independently. In fact, you can double the value you get from simply considering the one dimensional case. That should make this problem trivial IMO.
$endgroup$
– Don Thousand
4 hours ago
1
$begingroup$
This post from MSE applies here. If your lecturer gave you this question, (s)he must think that you should be able to gain something by trying it yourself. Having other people do it for you will gain you nothing at all.
$endgroup$
– Arnaud Mortier
2 hours ago
2
2
$begingroup$
Is this a question that comes from somewhere else, or one you've made up?
$endgroup$
– Gareth McCaughan♦
5 hours ago
$begingroup$
Is this a question that comes from somewhere else, or one you've made up?
$endgroup$
– Gareth McCaughan♦
5 hours ago
$begingroup$
Isn't Manhattan distance the minimum number of moves for (not a rook, but) a piece that moves like a rook but only one square at a time? Or, equivalently, like a king but not diagonally.
$endgroup$
– Gareth McCaughan♦
5 hours ago
$begingroup$
Isn't Manhattan distance the minimum number of moves for (not a rook, but) a piece that moves like a rook but only one square at a time? Or, equivalently, like a king but not diagonally.
$endgroup$
– Gareth McCaughan♦
5 hours ago
3
3
$begingroup$
Hi @Pitcher_21, welcome to Puzzling SE! Like Gareth commented, this appears to be a problem you got from some other source other than yourself. If it is, can you include the source in your question? Thanks!
$endgroup$
– PiIsNot3
5 hours ago
$begingroup$
Hi @Pitcher_21, welcome to Puzzling SE! Like Gareth commented, this appears to be a problem you got from some other source other than yourself. If it is, can you include the source in your question? Thanks!
$endgroup$
– PiIsNot3
5 hours ago
1
1
$begingroup$
Note that taxicab distance is simply the sum of the distances on each dimension, so you can treat each independently. In fact, you can double the value you get from simply considering the one dimensional case. That should make this problem trivial IMO.
$endgroup$
– Don Thousand
4 hours ago
$begingroup$
Note that taxicab distance is simply the sum of the distances on each dimension, so you can treat each independently. In fact, you can double the value you get from simply considering the one dimensional case. That should make this problem trivial IMO.
$endgroup$
– Don Thousand
4 hours ago
1
1
$begingroup$
This post from MSE applies here. If your lecturer gave you this question, (s)he must think that you should be able to gain something by trying it yourself. Having other people do it for you will gain you nothing at all.
$endgroup$
– Arnaud Mortier
2 hours ago
$begingroup$
This post from MSE applies here. If your lecturer gave you this question, (s)he must think that you should be able to gain something by trying it yourself. Having other people do it for you will gain you nothing at all.
$endgroup$
– Arnaud Mortier
2 hours ago
|
show 2 more comments
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2
$begingroup$
Is this a question that comes from somewhere else, or one you've made up?
$endgroup$
– Gareth McCaughan♦
5 hours ago
$begingroup$
Isn't Manhattan distance the minimum number of moves for (not a rook, but) a piece that moves like a rook but only one square at a time? Or, equivalently, like a king but not diagonally.
$endgroup$
– Gareth McCaughan♦
5 hours ago
3
$begingroup$
Hi @Pitcher_21, welcome to Puzzling SE! Like Gareth commented, this appears to be a problem you got from some other source other than yourself. If it is, can you include the source in your question? Thanks!
$endgroup$
– PiIsNot3
5 hours ago
1
$begingroup$
Note that taxicab distance is simply the sum of the distances on each dimension, so you can treat each independently. In fact, you can double the value you get from simply considering the one dimensional case. That should make this problem trivial IMO.
$endgroup$
– Don Thousand
4 hours ago
1
$begingroup$
This post from MSE applies here. If your lecturer gave you this question, (s)he must think that you should be able to gain something by trying it yourself. Having other people do it for you will gain you nothing at all.
$endgroup$
– Arnaud Mortier
2 hours ago