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This thought experiment gets even wilder if you like to live dangerously and leave two jokers and the rules card in the deck. 55 factorial is even larger

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The jokers are indistinguishable, so it's only 55 factorial divided by two.

Sometimes they are distinct, usually one is black & white and the other is color.. the solitaire cipher makes use of this distinction.

Solitaire: https://en.wikipedia.org/wiki/Solitaire_(cipher)

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