Drawing loops on a sheet of paper
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3
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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
edited 4 hours ago
rhsquared
6,73521641
asked 5 hours ago
Stefan
1315
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Stefan 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 |
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
edited 4 hours ago
rhsquared
6,73521641
asked 5 hours ago
Stefan
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.
Are the loops circles? Or any closed shape?
– Dr Xorile
1 hour ago
Any closed shape.
– Stefan
1 hour ago
add a comment |
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
edited 4 hours ago
rhsquared
6,73521641
asked 5 hours ago
Stefan
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.
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
edited 4 hours ago
rhsquared
6,73521641
asked 5 hours ago
Stefan
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.
edited 4 hours ago
rhsquared
6,73521641
asked 5 hours ago
Stefan
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.
edited 4 hours ago
rhsquared
6,73521641
edited 4 hours ago
rhsquared
6,73521641
edited 4 hours ago
rhsquared
6,73521641
6,73521641
asked 5 hours ago
Stefan
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.
asked 5 hours ago
Stefan
1315
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
add a comment |
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
add a comment |
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.
answered 52 mins ago
Dr Xorile
11k12263
add a comment |
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.
answered 52 mins ago
Dr Xorile
11k12263
add a comment |
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.
answered 52 mins ago
Dr Xorile
11k12263
add a comment |
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.
answered 52 mins ago
Dr Xorile
11k12263
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.
answered 52 mins ago
Dr Xorile
11k12263
answered 52 mins ago
Dr Xorile
11k12263
answered 52 mins ago
Dr Xorile
11k12263
answered 52 mins ago
Dr Xorile
11k12263
11k12263
add a comment |
add a comment |
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.
Stefan is a new contributor. Be nice, and check out our Code of Conduct.
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Are the loops circles? Or any closed shape?
– Dr Xorile
1 hour ago
Any closed shape.
– Stefan
1 hour ago