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You are presented the following six cards.

enter image description here

The red cards are rotations of F, and the blue cards are rotations of ꟻ (backwards F). Your goal is to make it so that the red cards are rotations of ꟻ (backwards F) and the blue cards are rotations of F in the minimal number of moves.

Allowed moves:

  • Rotate a blue card 90 degrees clockwise
  • Flip a blue card horizontally (e.g. b becomes d)
  • Flip a red card vertically (e.g. P becomes b)

Restrictions:

  • At no time may any two cards look the same ignoring color.
  • At no time may any card look like a normal F. Only a rotation or reflection thereof.
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  • 1
    $\begingroup$ @QuantumTwinkie Only because I can't find a Unicode character for an upside-down F. So I'm using P as an example instead. The example would not occur with the actual cards. I'm just using it to accurately demonstrate what "flip vertically" means. $\endgroup$ – Riley May 27 '18 at 15:11
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    $\begingroup$ @QuantumTwinkie Did I say you can rotate the red cards? :) $\endgroup$ – Riley May 27 '18 at 15:25
  • $\begingroup$ FYI, the reversed-F symbol isn't showing up correctly on my screen: i.stack.imgur.com/2Z6mI.png $\endgroup$ – Rand al'Thor May 27 '18 at 16:09
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    $\begingroup$ @noedne Yes, it looks like "Red Fish Blue [little box with symbols] ish". $\endgroup$ – Rand al'Thor May 27 '18 at 16:17
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    $\begingroup$ @noedne I'd rather leave the title as it is, since it's not important in solving the puzzle. $\endgroup$ – Riley May 27 '18 at 16:17
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I think I can do it in $10$ moves as follows: rotate b3, rotate b1, flip r3, flip b3, rotate b1, flip r1, flip b2, flip r2, rotate b3, flip b1. I do not have good pictures of this process.

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  • $\begingroup$ After you flip r2, I believe r2 and b2 look the same, violating the restriction. $\endgroup$ – Riley May 27 '18 at 15:46
  • $\begingroup$ @Riley Oops, I think I confused r2 and r3. $\endgroup$ – noedne May 27 '18 at 15:48

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