## LIGHTS OUT

This solution does not guarantee the least number of moves per pattern, but LIGHTS OUT allows you to exceed that number by 10 extra moves, so you should be OK.

### Notation:

LIGHTS OUT has a 5x5 array of buttons, which I will represent using an HTML formatted table. The squares will be numbered from 01 to 25, where:

BOLD = light ON,
italic = light OFF, and
* = button to press. For example:

 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Lights #01, 05, 07, 09, 13, 17, 19, 21 & 25 are ON, while the rest are OFF.

### Solution:

#### I. Eliminate the top row

For every light that is ON in the top row, press the button directly below it.
For example:

 01 02 03 04 05 ...press buttons#06 & 10,resulting with... 01 02 03 04 05 06* 07 08 09 10* 06 07 08 09 10 11 12 13 14 15 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 21 22 23 24 25 21 22 23 24 25

All the lights in the top row will then be OFF.

#### II. Eliminate the 2nd row

For every light that is ON in the 2nd row, press the button directly below it.
Continuing with the example:

 01 02 03 04 05 ...press buttons#11 & 15,resulting with... 01 02 03 04 05 06 07 08 09 10 06 07 08 09 10 11* 12 13 14 15* 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 21 22 23 24 25 21 22 23 24 25

All the lights in the 2nd row will then be OFF.

#### III. Eliminate the 3rd row

For every light that is ON in the 3rd row, press the button directly below it.
Continuing with the example:

 01 02 03 04 05 ...press buttons#17, 18 & 19,resulting with... 01 02 03 04 05 06 07 08 09 10 06 07 08 09 10 11 12 13 14 15 11 12 13 14 15 16 17* 18* 19* 20 16 17 18 19 20 21 22 23 24 25 21 22 23 24 25

All the lights in the 3rd row will then be OFF.

#### IV. Eliminate the 4th row

For every light that is ON in the 4th row, press the button directly below it.
Continuing with the example:

 01 02 03 04 05 ...press buttons#17, 18 & 19,resulting with... 01 02 03 04 05 06 07 08 09 10 06 07 08 09 10 11 12 13 14 15 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 21 22* 23* 24* 25 21 22 23 24 25

All the lights in the 4th row will then be OFF, and only the bottom row has lights that are still ON.
This method is known as "chasing down the lights".

Unfortunately, we cannot eliminate the bottom row as before... there are simply no buttons below it! The bottom row does provide a clue, which I call a signature. The signature is the pattern of lights remaining on in the bottom row. Believe it or not, there are only 7 possible combinations. Read the signature on the bottom row, and match it with the table below:

 If the signatureon the bottom rowlooks like this: ...with these lights on: ...then press the buttons: ...on the top row. #21 & 25 #01 & 02 01* 02* 03 04 05 21 22 23 24 25 #22 & 24 #01 & 04 01* 02 03 04* 05 21 22 23 24 25 #21, 22 & 23 #02 01 02* 03 04 05 21 22 23 24 25 #23, 24 & 25 #04 01 02 03 04* 05 21 22 23 24 25 #21, 23 & 24 #05 01 02 03 04 05* 21 22 23 24 25 #22, 23 & 25 #01 01* 02 03 04 05 21 22 23 24 25 #21, 22, 24 & 25 #03 01 02 03* 04 05 21 22 23 24 25

Hint: Hit the START button before pressing any buttons on the top row. Even though this will reset the puzzle, it will in turn reset the move-count to zero, and the puzzle can then be solved by merely "chasing down the lights".

#### VI. Enter the code

If you haven't already, go ahead and press the button(s) on the first row according to the table above. In our example puzzle, the bottom row had lights #22 and 24 ON. Therefore, we should press buttons #01 and 04 on the top row:

 01* 02 03 04* 05 ...press buttons#01 & 04,resulting with... 01 02 03 04 05 06 07 08 09 10 06 07 08 09 10 11 12 13 14 15 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 21 22 23 24 25 21 22 23 24 25

#### VII. Eliminate rows (again)

Eliminate the first 4 rows using the same method as before. Continuing with the example:

 01 02 03 04 05 ...press button#06, 07, 08,09 & 10resulting with... 01 02 03 04 05 06* 07* 08* 09* 10* 06 07 08 09 10 11 12 13 14 15 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 21 22 23 24 25 21 22 23 24 25

...eliminates the top row.

 01 02 03 04 05 ...press button#11, 12 & 13resulting with... 01 02 03 04 05 06 07 08 09 10 06 07 08 09 10 11* 12* 13* 14 15 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 21 22 23 24 25 21 22 23 24 25

...eliminates the 2nd row.

 01 02 03 04 05 ...press button#16, 18 & 20resulting with... 01 02 03 04 05 06 07 08 09 10 06 07 08 09 10 11 12 13 14 15 11 12 13 14 15 16* 17 18* 19 20* 16 17 18 19 20 21 22 23 24 25 21 22 23 24 25

...eliminates the 3rd row.

 01 02 03 04 05 ...press button#22 & 25resulting with... 01 02 03 04 05 06 07 08 09 10 06 07 08 09 10 11 12 13 14 15 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 21 22* 23 24 25* 21 22 23 24 25

...eliminates the 4th AND bottom row. As a matter of fact, ALL the lights are off! The puzzle is solved.