Here’s a problem a friend of mine posed to me a long time ago, that I was recently reminded of. I figured, with modern computing, there might be some way to figure it out:
Assume that there are two set of 52 cards, 13 of each of four sets. Now, for the purpose of a game, each card of the first deck becomes associated with one card in the other card such that, say, A♠ = 5♣.
The second set follows these conditions: 1.) No card may be it’s own twin 2.) No card may appear twice 3.) Four of a kind in the normal deck may not repeat suits in the second deck. 4.) Any poker run in a normal deck (straight, flush) must be disrupted in the second.
Is there a set of cards that matches these conditions? And if so, what is it?