The possibility of swapping a value to a different value (absolute difference is two)

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












For example, the original vector is (2, 4, 1, 0).



After swapping, it can be (1, 0, 2, 4) or (0, 1, 4, 2).



The second outcome is what I want because every absolute value of the difference between the original values and the new values are equal to or more than 2, say|2-0|=2, |4-1|>2, |1-4|>2, |0-2|=2.



However, the first outcome is not what I want because for example |2-1|<2.



How to decide whether the original vector can be swapped to a new vector where every absolute value of the difference between the original values and the new values are equal to or more than 2?



Any suggestions? Many thanks.




probability combinatorics statistics optimization




share|cite|improve this question



















  • Any thoughts on the answer I posted yesterday?
    – Gerry Myerson
    yesterday










  • Earth to Orchard's, come in, please.
    – Gerry Myerson
    13 hours ago














up vote
0
down vote

favorite












For example, the original vector is (2, 4, 1, 0).



After swapping, it can be (1, 0, 2, 4) or (0, 1, 4, 2).



The second outcome is what I want because every absolute value of the difference between the original values and the new values are equal to or more than 2, say|2-0|=2, |4-1|>2, |1-4|>2, |0-2|=2.



However, the first outcome is not what I want because for example |2-1|<2.



How to decide whether the original vector can be swapped to a new vector where every absolute value of the difference between the original values and the new values are equal to or more than 2?



Any suggestions? Many thanks.




probability combinatorics statistics optimization




share|cite|improve this question



















  • Any thoughts on the answer I posted yesterday?
    – Gerry Myerson
    yesterday










  • Earth to Orchard's, come in, please.
    – Gerry Myerson
    13 hours ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











For example, the original vector is (2, 4, 1, 0).



After swapping, it can be (1, 0, 2, 4) or (0, 1, 4, 2).



The second outcome is what I want because every absolute value of the difference between the original values and the new values are equal to or more than 2, say|2-0|=2, |4-1|>2, |1-4|>2, |0-2|=2.



However, the first outcome is not what I want because for example |2-1|<2.



How to decide whether the original vector can be swapped to a new vector where every absolute value of the difference between the original values and the new values are equal to or more than 2?



Any suggestions? Many thanks.




probability combinatorics statistics optimization




share|cite|improve this question











For example, the original vector is (2, 4, 1, 0).



After swapping, it can be (1, 0, 2, 4) or (0, 1, 4, 2).



The second outcome is what I want because every absolute value of the difference between the original values and the new values are equal to or more than 2, say|2-0|=2, |4-1|>2, |1-4|>2, |0-2|=2.



However, the first outcome is not what I want because for example |2-1|<2.



How to decide whether the original vector can be swapped to a new vector where every absolute value of the difference between the original values and the new values are equal to or more than 2?



Any suggestions? Many thanks.





probability combinatorics statistics optimization





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked 2 days ago









Orchard's Story

1




1











  • Any thoughts on the answer I posted yesterday?
    – Gerry Myerson
    yesterday










  • Earth to Orchard's, come in, please.
    – Gerry Myerson
    13 hours ago
















  • Any thoughts on the answer I posted yesterday?
    – Gerry Myerson
    yesterday










  • Earth to Orchard's, come in, please.
    – Gerry Myerson
    13 hours ago















Any thoughts on the answer I posted yesterday?
– Gerry Myerson
yesterday




Any thoughts on the answer I posted yesterday?
– Gerry Myerson
yesterday












Earth to Orchard's, come in, please.
– Gerry Myerson
13 hours ago




Earth to Orchard's, come in, please.
– Gerry Myerson
13 hours ago










1 Answer
1






active

oldest

votes

















up vote
0
down vote













First, put your entries in increasing order, $a_1le a_2lecdotsle a_2n$. Then in your original vector swap $a_i$ with $a_n+i$ for each $i$. If that doesn't work, nothing will.



In your example, you go $0,1,2,4$, then swap $0$ with $2$, and $1$ with $4$ (as you did).



You have to fudge this a little, if your vector has an odd number of entries.






share|cite|improve this answer





















  • Hi, your approach seems good. What if the number of values is odd, say 1, 2, 3, 4, 5.
    – Orchard's Story
    12 hours ago











  • As I wrote, you have to fudge it a little. Why not think about it, and see whether you can figure out what to do? If you give it a go, but don't get anywhere, I'll come back to help.
    – Gerry Myerson
    5 hours ago










Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);








 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2871758%2fthe-possibility-of-swapping-a-value-to-a-different-value-absolute-difference-is%23new-answer', 'question_page');

);

Post as a guest

















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote













First, put your entries in increasing order, $a_1le a_2lecdotsle a_2n$. Then in your original vector swap $a_i$ with $a_n+i$ for each $i$. If that doesn't work, nothing will.



In your example, you go $0,1,2,4$, then swap $0$ with $2$, and $1$ with $4$ (as you did).



You have to fudge this a little, if your vector has an odd number of entries.






share|cite|improve this answer





















  • Hi, your approach seems good. What if the number of values is odd, say 1, 2, 3, 4, 5.
    – Orchard's Story
    12 hours ago











  • As I wrote, you have to fudge it a little. Why not think about it, and see whether you can figure out what to do? If you give it a go, but don't get anywhere, I'll come back to help.
    – Gerry Myerson
    5 hours ago














up vote
0
down vote













First, put your entries in increasing order, $a_1le a_2lecdotsle a_2n$. Then in your original vector swap $a_i$ with $a_n+i$ for each $i$. If that doesn't work, nothing will.



In your example, you go $0,1,2,4$, then swap $0$ with $2$, and $1$ with $4$ (as you did).



You have to fudge this a little, if your vector has an odd number of entries.






share|cite|improve this answer





















  • Hi, your approach seems good. What if the number of values is odd, say 1, 2, 3, 4, 5.
    – Orchard's Story
    12 hours ago











  • As I wrote, you have to fudge it a little. Why not think about it, and see whether you can figure out what to do? If you give it a go, but don't get anywhere, I'll come back to help.
    – Gerry Myerson
    5 hours ago












up vote
0
down vote










up vote
0
down vote









First, put your entries in increasing order, $a_1le a_2lecdotsle a_2n$. Then in your original vector swap $a_i$ with $a_n+i$ for each $i$. If that doesn't work, nothing will.



In your example, you go $0,1,2,4$, then swap $0$ with $2$, and $1$ with $4$ (as you did).



You have to fudge this a little, if your vector has an odd number of entries.






share|cite|improve this answer













First, put your entries in increasing order, $a_1le a_2lecdotsle a_2n$. Then in your original vector swap $a_i$ with $a_n+i$ for each $i$. If that doesn't work, nothing will.



In your example, you go $0,1,2,4$, then swap $0$ with $2$, and $1$ with $4$ (as you did).



You have to fudge this a little, if your vector has an odd number of entries.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered 2 days ago









Gerry Myerson

142k7142292




142k7142292











  • Hi, your approach seems good. What if the number of values is odd, say 1, 2, 3, 4, 5.
    – Orchard's Story
    12 hours ago











  • As I wrote, you have to fudge it a little. Why not think about it, and see whether you can figure out what to do? If you give it a go, but don't get anywhere, I'll come back to help.
    – Gerry Myerson
    5 hours ago
















  • Hi, your approach seems good. What if the number of values is odd, say 1, 2, 3, 4, 5.
    – Orchard's Story
    12 hours ago











  • As I wrote, you have to fudge it a little. Why not think about it, and see whether you can figure out what to do? If you give it a go, but don't get anywhere, I'll come back to help.
    – Gerry Myerson
    5 hours ago















Hi, your approach seems good. What if the number of values is odd, say 1, 2, 3, 4, 5.
– Orchard's Story
12 hours ago





Hi, your approach seems good. What if the number of values is odd, say 1, 2, 3, 4, 5.
– Orchard's Story
12 hours ago













As I wrote, you have to fudge it a little. Why not think about it, and see whether you can figure out what to do? If you give it a go, but don't get anywhere, I'll come back to help.
– Gerry Myerson
5 hours ago




As I wrote, you have to fudge it a little. Why not think about it, and see whether you can figure out what to do? If you give it a go, but don't get anywhere, I'll come back to help.
– Gerry Myerson
5 hours ago












 

draft saved


draft discarded


























 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2871758%2fthe-possibility-of-swapping-a-value-to-a-different-value-absolute-difference-is%23new-answer', 'question_page');

);

Post as a guest
































































Comments

Post a Comment

Popular posts from this blog

Color the edges and diagonals of a regular polygon

Image
Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne
Read more

Relationship between determinant of matrix and determinant of adjoint?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/… – Hector Blandin Nov 17 &
Read more

What is the equation of a 3D cone with generalised tilt?

Image
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an
Read more