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A box containing identical dice that were arranged to have same orientation has a missing die at the center (see figure). The dice moves to the free space for they can change orientation and position. To move by sliding is prevented by some wire mess but a die can roll up, down, left or right to the empty square next to it. How should the dice roll within the box so that all of them have a unique orientation?

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    $\begingroup$ But originally they already have a unique orientation, right? Do you want to roll them to a different orientation, or do you want to determine all possible rolling sequences that lead to a unique orientation? $\endgroup$ – WhatsUp Oct 11 '20 at 13:35
  • $\begingroup$ Assume standard western dice. All starting orientation of dice are Top-Front :(1-4). One of the dice may not need to be rolled. The problem requires the rolling sequence that make all individual die to have a different "Top-Front" orientation. $\endgroup$ – TSLF Oct 11 '20 at 15:48
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    $\begingroup$ Just to be clear: although the question text doesn't say how many dice or anything of the sort, you mean very specifically a 5x5 array of dice with the centre one removed, right? (So that there are 24 = 6x4 dice left over, the same as the number of possible orientations.) $\endgroup$ – Gareth McCaughan Oct 11 '20 at 17:33
  • $\begingroup$ @garethmccaughan I suspect that's the answer. Pigeonhole all the way... $\endgroup$ – Dr Xorile Oct 11 '20 at 18:00
  • $\begingroup$ Well, that can't be the answer since the question is "how do you make it so?". $\endgroup$ – Gareth McCaughan Oct 11 '20 at 20:54

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