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Puzzling

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    $\begingroup$ So one in three configurations are solvable, and we can rotate B, D, and G independently? (oh, by the way your count_zero could be replaced with arr.count(0)) $\endgroup$
    – Jonathan Allan
    Commented Nov 21, 2016 at 11:09
  • $\begingroup$ When you say "Notice that rotating A+D+F+I once results in rotating all gears once. So we can safely assume that I=0 and later rotate all gears once to compensate for this." it is odd, because in the puzzle I see, you can only rotate all "gears" (unless you lock something). $\endgroup$
    – Tokkot
    Commented Nov 21, 2016 at 11:35
  • 1
    $\begingroup$ I suggest you to write an executive summary in the beginning of your post, stating when (if and only statement) the configuration is solvable. Then the interested reader can go on and start reading the details. Now the answer is hidden deep down amongst the lines of the reasoning (=proof of the claim). $\endgroup$
    – Matsmath
    Commented Nov 21, 2016 at 11:38
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    $\begingroup$ So "almost always solvable" means "solvable with probability 1/3 if states are chosen randomly"? $\endgroup$
    – hmakholm left over Monica
    Commented Nov 21, 2016 at 14:01
  • $\begingroup$ Wow, I didn't know this answer attracts so much traction. I'll update the answer as your good and constructive comments suggested. $\endgroup$
    – justhalf
    Commented Nov 22, 2016 at 2:06