Lights out puzzle

[ambrus]

Here's a quick Monday morning puzzle.

You have a 14x14 rectangular game board except that the last 7 fields of the last row are missing. Each field has a lamp, and a button that toggles the lamps on that field and each of its neighbours in a cardinal direction, altogether at most five lamps. At the start, all lights are lit. Find out which buttons to push to unlight all lights.

Why I like this puzzle is:

<Reveal this spoiler or all spoilers in this node or all in this thread>

Solution:

<Reveal this spoiler>

Update: here's an example. Suppose we have a 3x4 board with the last 1 field of the last row missing. At the start, it looks like this, all lamps lit:

 ****
 ****
 ***

Now we press the button on the bottom left field so three lights go off:

 ****
 .***
 ..*

then press the button above that so two lights turn back on but two lights go off:

 .***
 *.**
 *.*

now press the second button in the bottom row:

 .***
 ****
 .*.

now the button above that one:

 ..**
 ...*
 ...

finally press the top right button:

....
....
...

and all the lights are off, so we've solved this small board.