Drawing loops on a sheet of paper











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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







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  • Are the loops circles? Or any closed shape?
    – Dr Xorile
    2 hours 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
    2 hours 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




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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.
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asked 6 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
    2 hours ago










  • Any closed shape.
    – Stefan
    1 hour ago


















  • Are the loops circles? Or any closed shape?
    – Dr Xorile
    2 hours ago










  • Any closed shape.
    – Stefan
    1 hour ago
















Are the loops circles? Or any closed shape?
– Dr Xorile
2 hours ago




Are the loops circles? Or any closed shape?
– Dr Xorile
2 hours 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.







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    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 1 hour ago









        Dr Xorile

        11k12263




        11k12263






















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










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