Labelling a Snow Flake Graph to Attain Minimum Sum












2












$begingroup$


Label the vertices (or nodes) of this graph with positive integers so that any two nodes are joined by a edge (or line) if and only if the corresponding integers have a common divisor greater than 1 (i.e. they are not relatively prime). Do so in such a way that the total sum of the 13 numbers is minimum.



enter image description here






mathematics computer-puzzle arithmetic







share|improve this question











$endgroup$












  • $begingroup$
    computer-puzzle? Hmm, maybe this is harder than I was expecting.
    $endgroup$
    – Hugh
    5 hours ago












  • $begingroup$
    must the numbers be distinct? thanks!
    $endgroup$
    – Omega Krypton
    5 hours ago










  • $begingroup$
    @Omega Kyrpton: By necessity!
    $endgroup$
    – Bernardo Recamán Santos
    5 hours ago
















2












$begingroup$


Label the vertices (or nodes) of this graph with positive integers so that any two nodes are joined by a edge (or line) if and only if the corresponding integers have a common divisor greater than 1 (i.e. they are not relatively prime). Do so in such a way that the total sum of the 13 numbers is minimum.



enter image description here






mathematics computer-puzzle arithmetic







share|improve this question











$endgroup$












  • $begingroup$
    computer-puzzle? Hmm, maybe this is harder than I was expecting.
    $endgroup$
    – Hugh
    5 hours ago












  • $begingroup$
    must the numbers be distinct? thanks!
    $endgroup$
    – Omega Krypton
    5 hours ago










  • $begingroup$
    @Omega Kyrpton: By necessity!
    $endgroup$
    – Bernardo Recamán Santos
    5 hours ago














2












2








2





$begingroup$


Label the vertices (or nodes) of this graph with positive integers so that any two nodes are joined by a edge (or line) if and only if the corresponding integers have a common divisor greater than 1 (i.e. they are not relatively prime). Do so in such a way that the total sum of the 13 numbers is minimum.



enter image description here






mathematics computer-puzzle arithmetic







share|improve this question











$endgroup$




Label the vertices (or nodes) of this graph with positive integers so that any two nodes are joined by a edge (or line) if and only if the corresponding integers have a common divisor greater than 1 (i.e. they are not relatively prime). Do so in such a way that the total sum of the 13 numbers is minimum.



enter image description here






mathematics computer-puzzle arithmetic




mathematics computer-puzzle arithmetic






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 5 hours ago







Bernardo Recamán Santos

















asked 5 hours ago









Bernardo Recamán SantosBernardo Recamán Santos

2,4051343




2,4051343












  • $begingroup$
    computer-puzzle? Hmm, maybe this is harder than I was expecting.
    $endgroup$
    – Hugh
    5 hours ago












  • $begingroup$
    must the numbers be distinct? thanks!
    $endgroup$
    – Omega Krypton
    5 hours ago










  • $begingroup$
    @Omega Kyrpton: By necessity!
    $endgroup$
    – Bernardo Recamán Santos
    5 hours ago


















  • $begingroup$
    computer-puzzle? Hmm, maybe this is harder than I was expecting.
    $endgroup$
    – Hugh
    5 hours ago












  • $begingroup$
    must the numbers be distinct? thanks!
    $endgroup$
    – Omega Krypton
    5 hours ago










  • $begingroup$
    @Omega Kyrpton: By necessity!
    $endgroup$
    – Bernardo Recamán Santos
    5 hours ago
















$begingroup$
computer-puzzle? Hmm, maybe this is harder than I was expecting.
$endgroup$
– Hugh
5 hours ago






$begingroup$
computer-puzzle? Hmm, maybe this is harder than I was expecting.
$endgroup$
– Hugh
5 hours ago














$begingroup$
must the numbers be distinct? thanks!
$endgroup$
– Omega Krypton
5 hours ago




$begingroup$
must the numbers be distinct? thanks!
$endgroup$
– Omega Krypton
5 hours ago












$begingroup$
@Omega Kyrpton: By necessity!
$endgroup$
– Bernardo Recamán Santos
5 hours ago




$begingroup$
@Omega Kyrpton: By necessity!
$endgroup$
– Bernardo Recamán Santos
5 hours ago










1 Answer
1






active

oldest

votes


















0












$begingroup$

I believe that this task is...



impossible



I don't know how to write a formal proof, but here are some illustrations I hope can explain the case.



a, b, c, d, e, and f are distinct prime numbers. blue lines are lines that would need to be added. the two illustrations show two different cases.




! case 1
001
case 2:
002



!







share|improve this answer









$endgroup$













    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: "559"
    };
    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',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    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%2fpuzzling.stackexchange.com%2fquestions%2f79392%2flabelling-a-snow-flake-graph-to-attain-minimum-sum%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0












    $begingroup$

    I believe that this task is...



    impossible



    I don't know how to write a formal proof, but here are some illustrations I hope can explain the case.



    a, b, c, d, e, and f are distinct prime numbers. blue lines are lines that would need to be added. the two illustrations show two different cases.




    ! case 1
    001
    case 2:
    002



    !







    share|improve this answer









    $endgroup$


















      0












      $begingroup$

      I believe that this task is...



      impossible



      I don't know how to write a formal proof, but here are some illustrations I hope can explain the case.



      a, b, c, d, e, and f are distinct prime numbers. blue lines are lines that would need to be added. the two illustrations show two different cases.




      ! case 1
      001
      case 2:
      002



      !







      share|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        I believe that this task is...



        impossible



        I don't know how to write a formal proof, but here are some illustrations I hope can explain the case.



        a, b, c, d, e, and f are distinct prime numbers. blue lines are lines that would need to be added. the two illustrations show two different cases.




        ! case 1
        001
        case 2:
        002



        !







        share|improve this answer









        $endgroup$



        I believe that this task is...



        impossible



        I don't know how to write a formal proof, but here are some illustrations I hope can explain the case.



        a, b, c, d, e, and f are distinct prime numbers. blue lines are lines that would need to be added. the two illustrations show two different cases.




        ! case 1
        001
        case 2:
        002



        !








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 4 hours ago









        Omega KryptonOmega Krypton

        3,7641338




        3,7641338






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Puzzling Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f79392%2flabelling-a-snow-flake-graph-to-attain-minimum-sum%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            How to label and detect the document text images

            Image
            1 $begingroup$ This is what I mean as document text image: I want to label the texts in image as separate blocks and my model should detect these labels as classes. NOTE: This is how the end result should be like: The labels like Block 1, Block 2, Block 3,.. should be Logo, Title, Date,.. Others, etc. Work done: First approach : I tried to implement this method via Object Detection, it didn't work. It didn't even detect any text. Second approach : Then I tried it using PixelLink. As this model is build for scene text detection, it detected each and every text in the image. But this method can detect multiple lines of text if the threshold values are increased. But I have no idea how do I add labels to the text blocks. PIXEL_CLS_WEIGHT_all_ones = 'PIXEL_CLS_WEIGHT_all_ones' PIXEL_C...
            Read more

            Vallis Paradisi

            Image
            Coordinata: .mw-parser-output .geo-default,.mw-parser-output .geo-dms,.mw-parser-output .geo-dec{display:inline}.mw-parser-output .geo-nondefault,.mw-parser-output .geo-multi-punct{display:none}.mw-parser-output .longitude,.mw-parser-output .latitude{white-space:nowrap} 33°03′S 71°37′W  /  33.05°S 71.617°W  / -33.05; -71.617 Vallis Paradisi Res apud Vicidata repertae: Civitas : Chilia Numerus incolarum : 296 655 Zona horaria : UTC-4 Situs interretialis Nomen officiale : Valparaíso Gubernium Consilium : municipal council of Valparaíso Geographia Superficies : 401 600 000 Metrum quadratum Coniunctiones urbium Urbes gemellae : Ovetum , Badalona , Santa Fe , Ora longa , Sciamhaevum , Quantunia , Callao , Bat Yam , Melaka , Novorossiysk , Busan , Corduba , Odessa , Rosario , Malacca , Barcino , Soteropolis , Franciscopolis (California) , Guanajuato, Silao Tabula aut despectus Despectus in portum sinumque et urbem Vallis Paradisi Vallis Para...
            Read more

            Tabula Rosettana

            Image
            Tabula multilinguis Rosettana in Museo Britannico ostenditur. Tabula Rosettana, [1] etiam titulo OGIS 90 agnita, est stela decreto de rebus sacris in Aegypto anno 196 a.C.n. lato inscripta. Tabula iuxta Rosettam Aegypti, urbem in delta Nili et ad oram maris Mediterranei iacentem, anno 1799 a milite Francico reperta est. Inventio stelae, linguis duabus scripturisque tribus inscriptae, eruditis Instituti Aegypti statim nuntiata est; ibi enim iussu imperatoris Napoleonis eruditi omnium scientiarum (sub aegide Commissionis Scientiarum et Artium) properaverant cum expeditione Francica. Qua a Britannis mox debellata, tabula Rosettana Londinium missa hodie apud Museum Britannicum iacet. Textus Graecus cito lectus interpretationi textuum Aegyptiorum (in formis hieroglyphica et demotica expressorum) gradatim adiuvit. Denique textum plene interpretatus est Ioannes Franciscus Champollion. Ab opere eruditorum cumulativo coepit hodiernus scripturae hieroglyphicae linguaeque Aegyptiae a...
            Read more