Posts by EdV56

EdV56 · Help Me !

Hi,
can someone help me understand how the author arrived at 2222 rows for the exact cover matrix in this article?

Puzzling Over Exact Cover Problems

http://www.ams.org/samplings/feature-co … c-kanoodle

Given an exact cover matrix consisting of:

1. 67 columns: one for each of the 12 Kanoodle pieces and one for each cell in the 5 by 11 grid.

2. 12 Rows per solution corresponding to the 12 Kanoodle pieces.

3. A solution is 12 pieces placed filling the 5 by 11 grid

"We will therefore have one row in our matrix for each possible placement of each of the 12 pieces, which leads to 2222 rows."

I don't understand how the author arrived at 2222 rows

Thanks!

EdV56 · This is Cool

I am fine with it moving if that seems a more appropriate venue for discussions.

Thanks much

I will also refine my questions regarding
Graphs of Tilings (specifically a simple trominoes puzzle)
http://web.calstatela.edu/faculty/sheubac/papers/Graphs%20of%20Tilings.pdf

EdV56 · This is Cool

There is very interesting approach here to graph theoretic methods for tiling trominoes which I think could shed some light but get lost in their notation around page three:
Graphs of Tilings (specifically a simple trominoes puzzle)
http://web.calstatela.edu/faculty/sheubac/papers/Graphs%20of%20Tilings.pdf

EdV56 · This is Cool

thanks!

EdV56 · This is Cool

1. A tree graph would describe the 240 solutions and reflect left and right due to the similar helix pieces. There are also as many 16 solutions that begin with the same three pieces in the same position which would become major branches off of the trunk.
reference - http://www.fam-bundgaard.dk/SOMA/NEWS/N030518.HTM

2. A weighted graph of the pieces "touching" in all 240 solutions would be a way to illustrate the constancy of some of the pieces.
reference - http://www.fam-bundgaard.dk/SOMA/NEWS/N990201.HTM

How do I post pictures? Rather than links to pictures . . . .

Thanks much.

EdV56 · This is Cool

http://en.wikipedia.org/wiki/Soma_cube

http://www.mathematische-basteleien.de/soma25.jpg

EdV56 · This is Cool

Hi,
I was hoping start a little discussion at Math Stack Exchange about tree graphs and recording/displaying solutions to the SOMA cube puzzle. you can see some of what I have been doing here:

http://math.stackexchange.com/questions/954037/can-i-record-soma-puzzle-solutions-with-tree-graphs

Not much activity other than me.

It seems reasonable to me that the solutions can be shown on a tree graph but:
1. How best to do it? Start with tables and then sort the tables before graphing?
2. How much information is needed? I think the piece color occupying which of 8 vertices may suffice.
3. Are other graph methods of use to:
a. determine a bound on the number of solutions?
b. determine allowable piece positions?

This is part of a Leonardo's Basement project to make hands on math activities for elementary schools. Some previous work can be seen here:
http://www.fam-bundgaard.dk/SOMA/NEWS/N060808.HTM

I realize this is quite a number of questions but I thought I would give this forum a try. If I need to refine my query please let me know.

Thanks much!

Math Is Fun Forum

#1 Help Me ! » Determining Number of Rows in an Exact Cover Matrix » 2014-11-04 07:16:17

#2 Re: This is Cool » Are There Graph Theoretic Methods for Polycube Puzzles? » 2014-11-04 03:29:06

#3 Re: This is Cool » Are There Graph Theoretic Methods for Polycube Puzzles? » 2014-11-03 15:37:44

#4 Re: This is Cool » Are There Graph Theoretic Methods for Polycube Puzzles? » 2014-10-18 01:35:57

#5 Re: This is Cool » Are There Graph Theoretic Methods for Polycube Puzzles? » 2014-10-18 01:22:43

#6 Re: This is Cool » Are There Graph Theoretic Methods for Polycube Puzzles? » 2014-10-17 14:29:51

#7 This is Cool » Are There Graph Theoretic Methods for Polycube Puzzles? » 2014-10-17 07:35:23

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