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 Post subject: An edgematching problem
PostPosted: Wed Feb 13, 2013 9:17 pm 
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Location: Somewhere Else
If we color the edges of a square on one side with up to 4 colors, A, B, C, and D, and count mirror images as distinct, there are 70 ways to do it. It's possible to match these in a 7x10 rectangle.

If we change the rules to require that A and B always match with each other, instead of themselves - for example, by replacing the colors with jigsaw-like shaped edges, so every A and B fit together, except at the edge - it is still possible to construct a rectangle.

If the other pair, C and D, also follow this rule (so every C matches a D and vice versa, except at the edge), can you still make a rectangle?


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 Post subject: Re: An edgematching problem
PostPosted: Sat Feb 16, 2013 4:43 am 
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Joined: Wed Mar 15, 2000 9:11 pm
Location: Delft, the Netherlands
Jared wrote:
If we color the edges of a square on one side with up to 4 colors, A, B, C, and D, and count mirror images as distinct, there are 70 ways to do it. It's possible to match these in a 7x10 rectangle.

If we change the rules to require that A and B always match with each other, instead of themselves - for example, by replacing the colors with jigsaw-like shaped edges, so every A and B fit together, except at the edge - it is still possible to construct a rectangle.

If the other pair, C and D, also follow this rule (so every C matches a D and vice versa, except at the edge), can you still make a rectangle?


Yes.
Code:
  B     A     A     C     D     A     B     D     D     C   
D   A B   A B   D C   C D   D C   A B   B A   A B   C D   C
  C     A     A     C     D     A     B     A     B     D   
  D     B     B     D     C     B     A     B     A     C   
D   B A   B A   B A   B A   B A   C D   A B   C D   D C   C
  A     B     D     A     C     A     C     A     A     B   
  B     A     C     B     D     B     D     B     B     A   
A   D C   A B   A B   C D   A B   C D   C D   D C   D C   B
  A     D     D     C     C     D     A     A     A     A   
  B     C     C     D     D     C     B     B     B     B   
C   B A   A B   C D   A B   C D   A B   B A   C D   B A   D
  B     C     A     D     A     C     D     B     D     B   
  A     D     B     C     B     D     C     A     C     A   
C   D C   C D   C D   B A   C D   D C   A B   B A   C D   D
  A     D     C     A     D     C     D     A     C     C   
  B     C     D     B     C     D     C     B     D     D   
C   C D   C D   C D   C D   D C   D C   C D   D C   C D   D
  B     B     B     B     B     B     D     B     B     B   
  A     A     A     A     A     A     C     A     A     A   
A   A B   A B   C D   A B   A B   D C   A B   C D   C D   B
  A     B     B     D     C     B     A     C     C     D   

The top/bottom edges and left/right edges of the rectangle match too.

_________________
Jaap

Jaap's Puzzle Page:
http://www.jaapsch.net/puzzles/


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 Post subject: Re: An edgematching problem
PostPosted: Sat Feb 16, 2013 10:41 am 
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Location: Somewhere Else
Thank you!

BTW, I used your Polyform Solver to help with a similar problem the other day. It's a very useful program!


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