I claim that no arrangement is possible in the case with cards ace through four.
_A_A_A_A_ (_ is any other card)
must be part of the arrangement. Now consider two cases:
the row starts and ends with aces - this is obviously not
possible, since that arrangement would only hold 7 cards, and we
there are cards to the left and right ...
No time to finish, but a partial...
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I think the history is something like this.
Start with 8 colours because 8 is a small power of 2. These are simple: bit 0 for red, bit 1 for green, bit 2 for blue, but 000 means grey rather than black because you're only controlling the foreground and not the background.
Then add another 8 colours. Actually, in the image here it looks as if 8-15 may be the ...