Calculate pairing in a rotational system

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











up vote
0
down vote

favorite












I'm not even sure how to word this question. So I'll explain it out.



I've got these values:




$A_1, A_2, B_1, B_2, B_3, C_1, C_2$,




I need



  • each $A$ to be paired with each $B$ and $C$

  • each $B$ with each $A$ and $C$

  • each $C$ with each $A$ and $B$

but they can only be paired with one other letter at a time (i.e. in one day).



Each permutation is exclusive, meaning when $A_1$ is paired with $B_1$. $A_2$ could be paired with $B_2$ or $B_3$ or $C_1$ or $C_2$ but not $A_1$.



But as many as possible need to be paired at the same time.



If I put that into the real world each number could represent a person and the letters represent a skill. On a Monday I want two people with each skill to work with each other and as many people as possible to be working together. In a rotational system every day until the first two people are pairing again.



So hopefully I could come up with some table that would show who is working with who when.




Mon | Tues | ..



$A_1B_1 | A_1B_2 |$

$A_2B_2 | C_1A_2 |$




Is this possible, what is the name of the type of algorithm this is formed from?



Also what is the answer :-)






algorithms permutations recursive-algorithms







share|cite|improve this question























  • This is a kind of experimental design problem; you might have luck looking at the literature for this subject. Sadly, your problem is not exactly pairwise coverage, for which good tools and algorithms exist.
    – Johannes Kloos
    Mar 15 '12 at 16:20










  • Do you mean I'd need one less B for pairwise coverage?
    – Blundell
    Mar 15 '12 at 16:55










  • Actually, pairwise coverage would mean that you want tuples A_i B_j C_k.
    – Johannes Kloos
    Mar 15 '12 at 17:36














up vote
0
down vote

favorite












I'm not even sure how to word this question. So I'll explain it out.



I've got these values:




$A_1, A_2, B_1, B_2, B_3, C_1, C_2$,




I need



  • each $A$ to be paired with each $B$ and $C$

  • each $B$ with each $A$ and $C$

  • each $C$ with each $A$ and $B$

but they can only be paired with one other letter at a time (i.e. in one day).



Each permutation is exclusive, meaning when $A_1$ is paired with $B_1$. $A_2$ could be paired with $B_2$ or $B_3$ or $C_1$ or $C_2$ but not $A_1$.



But as many as possible need to be paired at the same time.



If I put that into the real world each number could represent a person and the letters represent a skill. On a Monday I want two people with each skill to work with each other and as many people as possible to be working together. In a rotational system every day until the first two people are pairing again.



So hopefully I could come up with some table that would show who is working with who when.




Mon | Tues | ..



$A_1B_1 | A_1B_2 |$

$A_2B_2 | C_1A_2 |$




Is this possible, what is the name of the type of algorithm this is formed from?



Also what is the answer :-)






algorithms permutations recursive-algorithms







share|cite|improve this question























  • This is a kind of experimental design problem; you might have luck looking at the literature for this subject. Sadly, your problem is not exactly pairwise coverage, for which good tools and algorithms exist.
    – Johannes Kloos
    Mar 15 '12 at 16:20










  • Do you mean I'd need one less B for pairwise coverage?
    – Blundell
    Mar 15 '12 at 16:55










  • Actually, pairwise coverage would mean that you want tuples A_i B_j C_k.
    – Johannes Kloos
    Mar 15 '12 at 17:36












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I'm not even sure how to word this question. So I'll explain it out.



I've got these values:




$A_1, A_2, B_1, B_2, B_3, C_1, C_2$,




I need



  • each $A$ to be paired with each $B$ and $C$

  • each $B$ with each $A$ and $C$

  • each $C$ with each $A$ and $B$

but they can only be paired with one other letter at a time (i.e. in one day).



Each permutation is exclusive, meaning when $A_1$ is paired with $B_1$. $A_2$ could be paired with $B_2$ or $B_3$ or $C_1$ or $C_2$ but not $A_1$.



But as many as possible need to be paired at the same time.



If I put that into the real world each number could represent a person and the letters represent a skill. On a Monday I want two people with each skill to work with each other and as many people as possible to be working together. In a rotational system every day until the first two people are pairing again.



So hopefully I could come up with some table that would show who is working with who when.




Mon | Tues | ..



$A_1B_1 | A_1B_2 |$

$A_2B_2 | C_1A_2 |$




Is this possible, what is the name of the type of algorithm this is formed from?



Also what is the answer :-)






algorithms permutations recursive-algorithms







share|cite|improve this question















I'm not even sure how to word this question. So I'll explain it out.



I've got these values:




$A_1, A_2, B_1, B_2, B_3, C_1, C_2$,




I need



  • each $A$ to be paired with each $B$ and $C$

  • each $B$ with each $A$ and $C$

  • each $C$ with each $A$ and $B$

but they can only be paired with one other letter at a time (i.e. in one day).



Each permutation is exclusive, meaning when $A_1$ is paired with $B_1$. $A_2$ could be paired with $B_2$ or $B_3$ or $C_1$ or $C_2$ but not $A_1$.



But as many as possible need to be paired at the same time.



If I put that into the real world each number could represent a person and the letters represent a skill. On a Monday I want two people with each skill to work with each other and as many people as possible to be working together. In a rotational system every day until the first two people are pairing again.



So hopefully I could come up with some table that would show who is working with who when.




Mon | Tues | ..



$A_1B_1 | A_1B_2 |$

$A_2B_2 | C_1A_2 |$




Is this possible, what is the name of the type of algorithm this is formed from?



Also what is the answer :-)






algorithms permutations recursive-algorithms




algorithms permutations recursive-algorithms






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 3 at 11:06









José Carlos Santos

122k16101186




122k16101186










asked Mar 15 '12 at 16:10









Blundell

634




634











  • This is a kind of experimental design problem; you might have luck looking at the literature for this subject. Sadly, your problem is not exactly pairwise coverage, for which good tools and algorithms exist.
    – Johannes Kloos
    Mar 15 '12 at 16:20










  • Do you mean I'd need one less B for pairwise coverage?
    – Blundell
    Mar 15 '12 at 16:55










  • Actually, pairwise coverage would mean that you want tuples A_i B_j C_k.
    – Johannes Kloos
    Mar 15 '12 at 17:36
















  • This is a kind of experimental design problem; you might have luck looking at the literature for this subject. Sadly, your problem is not exactly pairwise coverage, for which good tools and algorithms exist.
    – Johannes Kloos
    Mar 15 '12 at 16:20










  • Do you mean I'd need one less B for pairwise coverage?
    – Blundell
    Mar 15 '12 at 16:55










  • Actually, pairwise coverage would mean that you want tuples A_i B_j C_k.
    – Johannes Kloos
    Mar 15 '12 at 17:36















This is a kind of experimental design problem; you might have luck looking at the literature for this subject. Sadly, your problem is not exactly pairwise coverage, for which good tools and algorithms exist.
– Johannes Kloos
Mar 15 '12 at 16:20




This is a kind of experimental design problem; you might have luck looking at the literature for this subject. Sadly, your problem is not exactly pairwise coverage, for which good tools and algorithms exist.
– Johannes Kloos
Mar 15 '12 at 16:20












Do you mean I'd need one less B for pairwise coverage?
– Blundell
Mar 15 '12 at 16:55




Do you mean I'd need one less B for pairwise coverage?
– Blundell
Mar 15 '12 at 16:55












Actually, pairwise coverage would mean that you want tuples A_i B_j C_k.
– Johannes Kloos
Mar 15 '12 at 17:36




Actually, pairwise coverage would mean that you want tuples A_i B_j C_k.
– Johannes Kloos
Mar 15 '12 at 17:36















active

oldest

votes











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%2f120534%2fcalculate-pairing-in-a-rotational-system%23new-answer', 'question_page');

);

Post as a guest






















active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f120534%2fcalculate-pairing-in-a-rotational-system%23new-answer', 'question_page');

);

Post as a guest
































































-

這個網誌中的熱門文章

How to combine Bézier curves to a surface?

圖片
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier cur...
閱讀完整內容

Mutual Information Always Non-negative

圖片
Clash Royale CLAN TAG #URR8PPP up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 '12 at 15:38 Cameron Buie 83.6k 7 71 154 asked Jun 17 '12 at 15:30 Omri 359 3 13 3 Convexity of the function $tmapsto tlog t$. – Did Jun 17 '12 at 15:33 In addition, the convexity properties require the coefficients in the linear combination sum 1. Then, as p(x,y) is a probability distribution, it fullfits such condition. – Francisco Javier Delgado Ceped Aug 10 at 18:44 add a comment  |  up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 ...
閱讀完整內容

Why am i infinitely getting the same tweet with the Twitter Search API?

圖片
up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia...
閱讀完整內容