Drawing loops on a sheet of paper











up vote
3
down vote

favorite












Two people are playing a game, in which each player takes turns drawing closed loops on a sheet of paper. Each new loop must intersect each of the other loops exactly twice. When one player has no moves available, the other player wins.



Is it possible for any of the players to ever win? If yes, how? If not, prove that it is impossible.






game







share|improve this question









New contributor




Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Are the loops circles? Or any closed shape?
    – Dr Xorile
    1 hour ago










  • Any closed shape.
    – Stefan
    1 hour ago















up vote
3
down vote

favorite












Two people are playing a game, in which each player takes turns drawing closed loops on a sheet of paper. Each new loop must intersect each of the other loops exactly twice. When one player has no moves available, the other player wins.



Is it possible for any of the players to ever win? If yes, how? If not, prove that it is impossible.






game







share|improve this question









New contributor




Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.




















  • Are the loops circles? Or any closed shape?
    – Dr Xorile
    1 hour ago










  • Any closed shape.
    – Stefan
    1 hour ago













up vote
3
down vote

favorite









up vote
3
down vote

favorite











Two people are playing a game, in which each player takes turns drawing closed loops on a sheet of paper. Each new loop must intersect each of the other loops exactly twice. When one player has no moves available, the other player wins.



Is it possible for any of the players to ever win? If yes, how? If not, prove that it is impossible.






game







share|improve this question









New contributor




Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Two people are playing a game, in which each player takes turns drawing closed loops on a sheet of paper. Each new loop must intersect each of the other loops exactly twice. When one player has no moves available, the other player wins.



Is it possible for any of the players to ever win? If yes, how? If not, prove that it is impossible.






game




game






share|improve this question









New contributor




Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 4 hours ago









rhsquared

6,73521641




6,73521641






New contributor




Stefan 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









Stefan

1315




1315




New contributor




Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Stefan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.












  • Are the loops circles? Or any closed shape?
    – Dr Xorile
    1 hour ago










  • Any closed shape.
    – Stefan
    1 hour ago


















  • Are the loops circles? Or any closed shape?
    – Dr Xorile
    1 hour ago










  • Any closed shape.
    – Stefan
    1 hour ago
















Are the loops circles? Or any closed shape?
– Dr Xorile
1 hour ago




Are the loops circles? Or any closed shape?
– Dr Xorile
1 hour ago












Any closed shape.
– Stefan
1 hour ago




Any closed shape.
– Stefan
1 hour ago










1 Answer
1






active

oldest

votes

















up vote
2
down vote



accepted











In theory, neither side can win.




This is because




Each player can follow a strategy of drawing a loop that follows parallel and close to the last loop drawn. The last loop goes through each other loop twice, so if you follow it closely enough your line will do so also. Then just make it switch over twice as you're following it around.







share|improve this answer





















    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',
    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
    });


    }
    });






    Stefan is a new contributor. Be nice, and check out our Code of Conduct.










    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f76250%2fdrawing-loops-on-a-sheet-of-paper%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








    up vote
    2
    down vote



    accepted











    In theory, neither side can win.




    This is because




    Each player can follow a strategy of drawing a loop that follows parallel and close to the last loop drawn. The last loop goes through each other loop twice, so if you follow it closely enough your line will do so also. Then just make it switch over twice as you're following it around.







    share|improve this answer

























      up vote
      2
      down vote



      accepted











      In theory, neither side can win.




      This is because




      Each player can follow a strategy of drawing a loop that follows parallel and close to the last loop drawn. The last loop goes through each other loop twice, so if you follow it closely enough your line will do so also. Then just make it switch over twice as you're following it around.







      share|improve this answer























        up vote
        2
        down vote



        accepted







        up vote
        2
        down vote



        accepted







        In theory, neither side can win.




        This is because




        Each player can follow a strategy of drawing a loop that follows parallel and close to the last loop drawn. The last loop goes through each other loop twice, so if you follow it closely enough your line will do so also. Then just make it switch over twice as you're following it around.







        share|improve this answer













        In theory, neither side can win.




        This is because




        Each player can follow a strategy of drawing a loop that follows parallel and close to the last loop drawn. The last loop goes through each other loop twice, so if you follow it closely enough your line will do so also. Then just make it switch over twice as you're following it around.








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 53 mins ago









        Dr Xorile

        11k12263




        11k12263






















            Stefan is a new contributor. Be nice, and check out our Code of Conduct.










            draft saved

            draft discarded


















            Stefan is a new contributor. Be nice, and check out our Code of Conduct.













            Stefan is a new contributor. Be nice, and check out our Code of Conduct.












            Stefan is a new contributor. Be nice, and check out our Code of Conduct.
















            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.





            Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


            Please pay close attention to the following guidance:


            • 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.


            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%2f76250%2fdrawing-loops-on-a-sheet-of-paper%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

            Accessing regular linux commands in Huawei's Dopra Linux

            Image
            4 Backstory: I have a Huawei HG8245 router in my house and I want to change the default username/password. I've tried following this guide but the config file always gets reset. My ISP isn't helping either so I'm looking for other ways to accomplish this. The router has telnet access so this seems like a way to change the credentials. The first shell I gain access to looks like this: WAP> Pressing "?" gives me a list of available commands which I've pasted here, the two interesting ones are "su" and "shell". I can't seem to get su access, even after logging in as root (challenge password prompt, and then nothing happens), but shell gives me a proper linux shell. WAP>shell BusyBox v1.18.4 (2017-12-26 17:06:34 CST) built-in shell (ash) Enter 'hel...
            Read more

            Can't connect RFCOMM socket: Host is down

            Image
            up vote 3 down vote favorite I have bluez 5.4.3 and I am attempting to communicate with a ble device through minicom. These two deceives (my computer and a bluno nano) are alreadt paired and this has been my method so far. #bluetoothctl # pair xx:xx:xx:xx:xx:xx # exit Everything is working well so far then... #sudo rfcomm connect /dev/rfcomm0 xx:xx:xx:xx:xx:xx 1 & [1] 3665 Can't connect RFCOMM socket: Host is down Does anyone know how to resolve this issue? Any help would be very much appreciated. bluetooth bluez share | improve this question asked Feb 9 '17 at 18:46 Brandon Knape 46 2 ...
            Read more

            Kernel panic - not syncing: Fatal Exception in Interrupt

            Image
            0 Every day this error occured on my pc, kernel panic error on interrupt, what will be the problem? linux-mint share asked 6 mins ago Vinod Selvin Vinod Selvin 1 1 New contributor Vinod Selvin is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct. add a comment ...
            Read more