## M12

### Solving the Puzzle

#### The fundamental fact about M12

M12 is based on a sharply 5-transitive group.
"5-transitive" means that any five numbers can appear on any five balls.
"Sharply 5-transitive" means that having pinned five numbers, the remaining 7 will be in only one configuration.
If the five numbers are on the balls with matching tags, all the remaining numbers will be, too, and the puzzle will be solved!

#### The basic strategy

Find several combinations of moves that leave some numbers fixed while mixing up the rest.
It is very useful to define those combinations as combo button definitions and study exactly what they do.
The explanation of combo buttons describes doing this with the
Right+Swap+Left+Swap combination.
Use combo moves, spins and swaps to move five numbers, usually one at a time, to their correct balls.
The trick is to find combo moves that work together well, preserving mostly the same positions.

It is also probably easiest if the balls you are targeting are next to one another.
For instance, if you are trying to get 1 through 5 in place, you can arrange to move 5 to the 1-ball,
and then use Right to move it onto the 2-ball at the beginning of the "protected" group of four balls (2 through 5).
Moving 5 to the 1-ball should be very easy;
if it is on the 0-ball, use Swap; otherwise just spin it around the ring to the 1-ball.
Next work on moving 4 to the 1-ball using only moves that leave 2 through 5 undisturbed,
and tick it in next to the 5, and so forth.

The trick is finding useful moves like that!
Some moves that only protect balls 2 through 4 or 3 through 5 might be helpful, too.

You will probably notices that moves that leave four numbers fixed
usually will move the remaining eight number in two cycles of four.
Having found one such move, you will probably need a different move that
leaves the "protected" four numbers fixed but mixes up the other numbers
between those two cycles.

#### Acclaim for Solving Quickly

When you reach the Home position from a random puzzle, M12 will announce this with
a sound (if you have sound effects enabled).
For a long solution, you will hear the "tada" sound, but if your solution is short
enough, the crowd will cheer!