Mathematics desk | ||
---|---|---|
< June 7 | << May | June | Jul >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hello!
Suppose I have a set of 24 edge matching Wang tiles, 1 for every possible arrangement of 4 colours on each tile. I am trying to convince myself that I cannot arrange them on a 6x4 grid with all internal edges matching. I know that it be done if the tiles are permitted any rotation but not if they are non-rotatable tiles. I am trying to use symmetry operations on the tile set to argue that it is not possible. For example, if I arrange 6 tiles with colour #1 on the top, I can then place above them all the tiles with #1 at the bottom. But from there any symmetry operation or combination of operations leads to duplicate tiles.
Am I on the right track?
Duomillia ( talk) 03:13, 8 June 2021 (UTC)
Edit: If I go at it with pen and paper I think there might be away. Stay tuned I’ll post if I find something. Duomillia ( talk) 04:01, 8 June 2021 (UTC)
Follow up question: Is it possible to arrange my 24 tiles so that not a one edge is adjacent to the same colour?
Duomillia (
talk)
02:00, 14 June 2021 (UTC)
The definition (per Injective function) is stated as . Isn't it an if and only if, since if a=b, then f(a) must equal f(b) or else f is not a function? Could someone clarify please? Nikolaih ☎️ 📖 21:47, 8 June 2021 (UTC)
Mathematics desk | ||
---|---|---|
< June 7 | << May | June | Jul >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hello!
Suppose I have a set of 24 edge matching Wang tiles, 1 for every possible arrangement of 4 colours on each tile. I am trying to convince myself that I cannot arrange them on a 6x4 grid with all internal edges matching. I know that it be done if the tiles are permitted any rotation but not if they are non-rotatable tiles. I am trying to use symmetry operations on the tile set to argue that it is not possible. For example, if I arrange 6 tiles with colour #1 on the top, I can then place above them all the tiles with #1 at the bottom. But from there any symmetry operation or combination of operations leads to duplicate tiles.
Am I on the right track?
Duomillia ( talk) 03:13, 8 June 2021 (UTC)
Edit: If I go at it with pen and paper I think there might be away. Stay tuned I’ll post if I find something. Duomillia ( talk) 04:01, 8 June 2021 (UTC)
Follow up question: Is it possible to arrange my 24 tiles so that not a one edge is adjacent to the same colour?
Duomillia (
talk)
02:00, 14 June 2021 (UTC)
The definition (per Injective function) is stated as . Isn't it an if and only if, since if a=b, then f(a) must equal f(b) or else f is not a function? Could someone clarify please? Nikolaih ☎️ 📖 21:47, 8 June 2021 (UTC)