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Marq's Website

Math

Solving that 5×5 light grid puzzle

Notes on notation

General notes

Definition of "button-status" (a1, b2, etc.)

Nature of = for button-status

Definition of + for button-status

Nature of + for button-status

Definition of "button-grid" (A, B, etc.)

Nature of = for button-grid

Definition of + for button-grid

Defintion of Z

Definition of En

E1 =
10000
00000
00000
00000
00000
E2 =
01000
00000
00000
00000
00000
E3 =
00100
00000
00000
00000
00000
E4 =
00010
00000
00000
00000
00000
E5 =
00001
00000
00000
00000
00000
E6 =
00000
10000
00000
00000
00000
E7 =
00000
01000
00000
00000
00000
E8 =
00000
00100
00000
00000
00000
E9 =
00000
00010
00000
00000
00000
E10 =
00000
00001
00000
00000
00000
E11 =
00000
00000
10000
00000
00000
E12 =
00000
00000
01000
00000
00000
E13 =
00000
00000
00100
00000
00000
E14 =
00000
00000
00010
00000
00000
E15 =
00000
00000
00001
00000
00000
E16 =
00000
00000
00000
10000
00000
E17 =
00000
00000
00000
01000
00000
E18 =
00000
00000
00000
00100
00000
E19 =
00000
00000
00000
00010
00000
E20 =
00000
00000
00000
00001
00000
E21 =
00000
00000
00000
00000
10000
E22 =
00000
00000
00000
00000
01000
E23 =
00000
00000
00000
00000
00100
E24 =
00000
00000
00000
00000
00010
E25 =
00000
00000
00000
00000
00001

Definition of Mn

M1 =
11000
10000
00000
00000
00000
M2 =
11100
01000
00000
00000
00000
M3 =
01110
00100
00000
00000
00000
M4 =
00111
00010
00000
00000
00000
M5 =
00011
00001
00000
00000
00000
M6 =
10000
11000
10000
00000
00000
M7 =
01000
11100
01000
00000
00000
M8 =
00100
01110
00100
00000
00000
M9 =
00010
00111
00010
00000
00000
M10 =
00001
00011
00001
00000
00000
M11 =
00000
10000
11000
10000
00000
M12 =
00000
01000
11100
01000
00000
M13 =
00000
00100
01110
00100
00000
M14 =
00000
00010
00111
00010
00000
M15 =
00000
00001
00011
00001
00000
M16 =
00000
00000
10000
11000
10000
M17 =
00000
00000
01000
11100
01000
M18 =
00000
00000
00100
01110
00100
M19 =
00000
00000
00010
00111
00010
M20 =
00000
00000
00001
00011
00001
M21 =
00000
00000
00000
10000
11000
M22 =
00000
00000
00000
01000
11100
M23 =
00000
00000
00000
00100
01110
M24 =
00000
00000
00000
00010
00111
M25 =
00000
00000
00000
00001
00011

Defintion of × for button-grid

Nature of + and × for button-grid

Representation of the puzzle with our new algebra

Proof that repeating the solution on a solved grid will produce the original puzzle

Reasoning to the method for solving the puzzle

Definition of P and Q

Defintion of & for button-status

Definition of & for button-grid

Nature of & for button-grid

Defintion of real() for button-grid

Defintion of abs() for button-grid

Continuing to reason to the method for solving the puzzle

Possible solutions for each elementry puzzle

ABB + PB + QB + (P + Q)Instructions for symmetrical use
00000
01000
00000
00000
00000
01010
11011
00010
11100
01000
00100
01110
11001
01001
00110
11111
01110
00010
01001
11101
10001
11011
11001
11100
10011
Rotate A and solution by same number of degrees, either 0, 90, 180, or 270.
00000
00000
00100
00000
00000
01101
10001
10110
00100
11000
00011
00100
01101
10001
10110
11000
00100
10110
10001
01101
10110
10001
01101
00100
00011
10001
00000
00000
00000
00000
00011
10101
10110
00100
11000
01101
00000
01101
10001
10110
10110
00000
10110
10001
01101
11000
10101
01101
00100
00011
Rotate A and solution by same number of degrees, either 0, 90, 180, or 270.
01010
00000
00000
00000
00000
00111
00000
00111
01010
11100
01001
10101
11100
11111
10010
10010
10101
00111
11111
01001
11100
00000
11100
01010
00111
Rotate A and solution by same number of degrees, either 0, 90, 180, or 270.
01000
00000
01000
00000
00000
11011
01000
00111
01010
11100
10101
11101
11100
11111
10010
01110
11101
00111
11111
01001
00000
01000
11100
01010
00111
First, flip or do not flip A and solution horizontally, then rotate A and solution by same number of degrees, either 0, 90, 180, or 270.
01000
00000
00000
00000
01000
11100
00010
11011
00010
11100
10010
10111
00000
10111
10010
01001
10111
11011
10111
01001
00111
00010
00000
00010
00111
First, flip or do not flip A and solution horizontally, then rotate A and solution by same number of degrees, either 0, 90, 180, or 270.
00100
00100
00000
00000
00000
00011
00000
00111
01010
11100
01101
10101
11100
11111
10010
10110
10101
00111
11111
01001
11000
00000
11100
01010
00111
Rotate A and solution by same number of degrees, either 0, 90, 180, or 270.
00100
00000
00000
00000
00100
10101
10001
01110
00100
00000
11011
00100
10101
10001
01110
00000
00100
01110
10001
10101
01110
10001
10101
00100
11011
Rotate A and solution by same number of degrees, either 0 or 90.

Q.E.D.
Marq Thompson

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Last Updated: 2009-05-02