Thanks in advance!

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]]>Solutions are:

. B

.B 3 2

.B 4 2 B

.B B

. B

.B 3 2 B

.B 4 2

.B B

.B B B

. 3 2

.B 4 2

.B B B

. B B

.B 3 2

.B 4 2

. B B

. B B

.B 3 2

.B 4 2

.B B B

. B B

.B 3 2

.B 4 2

. B B

. B B

.B 3 2

.B 4 2

.B B B

I believe that is all of them so following the same number convention.

0 or 1

0 or 1

0 or 1

0 or 1

0 or 1

#3

#2

0

1

#4

#2

0 or 1

0 or 1

1

0 or 1

0 or 1

Let me know if my calculations are incorrect.

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]]> [E][E][E][E][E][E][E][E][E]

[E][E][E][E][E][E][E][E][E]

[E][E][E][E][E][E][E][E][E]

[E][E][E][3][2][E][E][E][E]

[E][E][E][4][2][E][E][E][E]

[E][E][E][E][E][E][E][E][E]

[E][E][E][E][E][E][E][E][E]

[E][E][E][E][E][E][E][E][E]

3 2

4 2

with E being blank tiles.

This is the matrix I get with index left to right, top to bottom

3: 1 1 1 0 1 0 1 0 0 0 0 0

top 2: 0 1 1 1 0 1 0 1 0 0 0 0

bot 2: 0 0 0 0 0 1 0 1 0 1 0 1

4: 0 0 0 0 1 0 1 0 1 1 1 0

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]]>But, at any rate, you can go and play 3D minesweeper if you like: http://egraether.com/mine3d/ (People have thought of this before ðŸ™‚ )

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]]>Has anyone considered 3 dimensional mine sweeper? What about n-dimensional?

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]]>I also added an aggressive “zero chaser”.

The “problem” I run into, sometimes, is having more rows than non-RHS columns going into the Gaussian elimination. Right now I stop adding rows when the number of rows equals the number of non-RHS columns, but am concerned I might be leaving something important out.

Here’s an example… Say the grid is as follows, where letters indicate an unknown square (there are no marked squares):

0 1 A C

0 1 B 1

0 1 1 1

D 0 E 0

My algorithm generates the following matrix for Gaussian elimination (after weeding out duplicated rows):

A B C D E | rhs

1 1 0 0 0 | 1

1 1 1 0 0 | 1

0 0 0 1 0 | 0

0 1 0 1 1 | 1

0 1 0 0 1 | 1

0 0 0 1 1 | 0

0 0 0 0 1 | 0

So that’s 5 unknowns and 7 unique equations.

As I said, right now I clip the rows after the fifth one since there are 5 unknowns. But I realize now after typing this all in is that what I need to do is check each candidate row with the upper/lower bounds algorithm and cover or flag squares right then if possible instead of adding it to the matrix for Gaussian elimination. That’ll make the overall run to completion all the faster.

Thanks for your attention, for replying, and for the great article! It’s been great fun working on it.

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