Re: [math-fun] domino networks... correction
Yesterday I wrote:
If we allow holes, I like the 5x6 with two holes. There's only one distinct such pattern, [...]
Nonsense. There are three. My program says: With the two holes at the corners on a long side, 0 solutions. With the two holes at diagonally opposite corners, 1 distinct solution, in yesterday's email. With the two holes at the corners on a short side, 9 distinct solutions: 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 3 3 4 4 5 3 3 4 4 5 3 3 4 5 1 3 3 4 5 1 3 3 4 5 1 6 7 8 6 1 6 7 8 6 1 6 2 4 6 6 6 2 4 6 6 6 7 4 6 6 6 2 5 5 7 6 5 2 2 7 7 2 8 8 9 7 2 8 8 9 8 7 2 2 9 9 2 3 9 7 9 5 3 9 7 1 9 3 7 9 7 9 3 7 1 1 9 3 8 9 1 8 8 9 4 1 8 8 9 4 8 5 5 7 4 4 9 5 5 8 7 5 5 8 4 1 1 2 1 2 3 1 2 3 1 2 3 3 3 4 5 1 2 4 5 3 4 2 4 5 3 4 3 4 2 5 5 6 7 4 6 6 6 4 7 8 8 6 4 7 8 8 6 4 7 7 8 8 7 2 2 9 6 9 1 1 5 8 9 1 1 5 6 5 1 6 2 8 9 3 8 1 8 9 3 6 5 2 9 3 6 5 9 9 1 8 9 4 9 5 5 7 2 2 7 7 9 2 7 7 6 9 7 3 3 8 4 -- Mike
I found an early reference. David Wells, Games and Puzzles, April 1976, page 31 Dominimum puzzle. He asks readers to fit the double-6 dominoes into a 4x5 grid. 3 dominoes are duplicated. --Ed Pegg Jr
Thanks for the reference, Ed!! And it contains a puzzle within a puzzle -- which 3 are duplicated, and are there solutions with some other 3 duplicated? For that matter, how many distinct ways can 3 of the double-6 set be duplicated? Meanwhile, my program found several distinct solutions to the smallest rectangular domino network with any solutions, a double-10 set (1..11, or blank..10) on a 4x10. There probably are many solutions. One is: 1 1 2 2 3 4 4 5 2 6 7 3 8 9 1 6 8 4 10 8 1 11 10 3 5 9 9 3 5 7 2 11 8 7 10 5 11 11 6 6 -- Mike ----- Original Message ----- From: "Ed Pegg Jr" <ed@mathpuzzle.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Sunday, September 12, 2010 5:45 PM Subject: Re: [math-fun] domino networks I found an early reference. David Wells, Games and Puzzles, April 1976, page 31 Dominimum puzzle. He asks readers to fit the double-6 dominoes into a 4x5 grid. 3 dominoes are duplicated. --Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (2)
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Ed Pegg Jr -
Michael Beeler