# Blithe 12

The purpose of the game, as with the Lucky 7 and Happy 8 puzzles, is to return
the counters into their *Home position*, position they were in before reshuffling. The puzzle consists of 12 counters
placed on three intersecting circles. There are six points of interaction: counters 1 and 4 control the left circle, counters 3 and 7 control
the right circle, counters 11 and 12 control the bottom one. Clicking on the two counters controlling a circle, rotate the counters on
that circle in opposite directions. Experiment with this before trying to solve a puzzle.

There are actually 5 puzzles in one. You can select from the following:

- 2 color puzzle
- 4 color puzzle, middle counters are the same
- 4 color puzzle, border counters are the same
- 6 color puzzle
- 12 number puzzle

For the last one, if the "Cycles" box is checked, a permutation of counters needed to solve the puzzle is displayed. The permutation is presented as a product of cycles.

In the case of 6 colors, each circle has been assigned a *pure* color (counters 1,4 for the first circle;
3,7 for second, and 11,12 for the third.) At the intersections colors have been selected in such a way as to have at the intersections
colors that appear to be mixtures of the colors of the corresponding circles.

Based on the theory of Permutations I can prove the following

### Theorem

The *Blithe12* puzzle is solvable for any starting configuration.

What if applet does not run? |

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