Shuffle Up and Deal - Riddler Classic
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From Matt Ginsberg, shuffle up and deal ⊠and rearrange ⊠and calculate:
You love to play cards. Bridge, spades, hearts, euchre, whist, setback, pitch, pinochle, bezique, sheepshead, écarté, krutzjass, baloot, königrufen ⊠you name it. If there are tricks to be taken, you want to take them.
You play so many card games that youâve developed a very specific organizational obsession. When youâre dealt your hand, you want to organize it such that the cards of a given suit are grouped together and, if possible, such that no suited groups of the same color are adjacent. (Numbers donât matter to you.) Moreover, when you receive your randomly ordered hand, you want to achieve this organization with a single motion, moving only one adjacent block of cards to some other position in your hand, maintaining the original order of that block and other cards, except for that one move.
Suppose youâre playing pitch, in which a hand has six cards. What are the odds that you can accomplish your obsessive goal? What about for another game, where a hand has N cards, somewhere between 1 and 13?
Editorâs note: Matt has no idea what the answer is (yet). His guess, for the record, is 57 percent.
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