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


The Blithe12 puzzle is solvable for any starting configuration.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

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Related material

Sliders and Puzzles on Graphs

  • Puzzles on graphs
  • Three Glass Puzzle (example)
  • Three Glass Puzzle in Barycentric Coordinates (example)
  • Sierpinski Gasket and Tower of Hanoi (example)
  • Sam Loyd's Fifteen
  • Slider Puzzles
  • Lucky 7
  • Happy 8
  • Proof of solvability of the Blithe 12 puzzle
  • Sliders, puzzles on graphs
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