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  Magicraft [cheats]
How to Solve 3×3 Puzzle (Lights Out Game):
------------------------------------------
The "9 plates you must turn on" puzzle is a game called "lights out".
From each position, there is a set of 0 or 1 steps that solve it,
turning all lights on. There are solvers online.

The main thing is that there are a few key positions that, once you
learn, you easily solve from there. For instance, if only a corner
is missing:
* 0XX
* XXX
* XXX

You need to step once on (and only on) these X-marqued plates to solve:
* XOX
* 00X
* XX0

Obviously, in case it’s another corner, you just rotate the pattern.

Other useful patterns are:
* OXX > XXX
* XOX > XXO
* XXX > XOO
* XOX > OXO
* XOX > XOX
* XXX > XOX
* XOX > OOO
* XXX > OXO
* XXX > XXX
* XXX > OXO
* XOX > XXX
* XXX > OXO

Most positions should be easily transposable into one of the above.
And then, you just solve for it.

-=Another Puzzle Solution=-
The "one with the paths" puzzle is a classic math problem called
"Konigsberg bridge problem".

The trick to solving is finding the two plates with odd numbers of paths
coming from it (there should be only two, or else it has no solution) ,
starting from one of them and finishing on the other. Given you start
and end on the odd plates, there should be multiple paths that work.

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