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Rubik's Clock


Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible configurations in total. The God's number (i.e., the graph diameter of the graph corresponding to Rubik's Clock, which is the minimum number of moves required to solve it from an arbitrary starting position-i.e., in the worst case) was shown by Kogler to be 12 (Kogler 2014; cube20.org).

The numbers of positions from which the clock can be solved in n=0, 1, ... moves are 1, 330, 51651, 4947912, 317141342, 14054473232, 428862722294, 8621633953202, 101600180118726, 528107928328516, 613251601892918, and 31893880879492, 39248 (A256586; cube20.org), which sum to 12^(14) as they must.


See also

God's Number, Rubik's Cube

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References

cube20.org. "Rubik's Clock Has Now Been Solved!" http://www.cube20.org/clock.Dénes, J. and Mullen, G. L. "Rubik's Clock and Its Solution." Math. Mag. 68, 378-381, 1995.Kogler, J. "God's Number for Clock Found." May 31, 2014. https://www.speedsolving.com/forum/showthread.php?47822-God-s-Number-for-Clock-found.Scherphuis, J. "Jaap's Puzzle Page: Rubik's Clock." http://www.geocities.com/jaapsch/puzzles/clock.htm.Sloane, N. J. A. Sequence A256586 in "The On-Line Encyclopedia of Integer Sequences."Zeilberger, D. "Doron Zeilberger's Maple Packages and Programs: RubikClock." http://www.math.temple.edu/~zeilberg/programs.html.

Referenced on Wolfram|Alpha

Rubik's Clock

Cite this as:

Weisstein, Eric W. "Rubik's Clock." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RubiksClock.html

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