Stefan G. Meyer
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- Joined
- Apr 26, 2014
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I'm looking for help with what I think is a mathematical problem, but I'm not sure what kind of mathematics is involved. At issue is a procedure done with an ordinary deck of 52 playing cards. Starting with the cards in a prearranged order, the deck is put through a controlled shuffle following certain precise steps, after which the cards, of course, will be in a different order. If the same procedure is done 90 times, the cards revert to their original order again. What I'm trying to determine is whether or not this procedure can be reduced to a mathematical equation whereby x equals the original order of the deck, which in turn equals a formula derived from an algorithm representing the procedure times 90. In other words, can an algorithm representing the procedure be translated in a numerical formula?
The numerical elements in this problem are quite simple: 52 cards in a deck (Joker is excluded) and 90 times for the procedure. The procedure itself is as follows:
1. The cards are put in a particular order. The order itself is only relevant for the purposes of checking to see if you are doing the operation correctly. To put them in an order that will allow you to easily check, put the cards down face up, starting with the A of Hearts, 2 of Hearts, 3 of Hearts, etc., all the way to the K of Hearts, then followed by the A of Clubs, 2 of Clubs, 3 of Clubs, etc., all the way to the K of Clubs, then the A of Diamonds all the way up to the K of Diamonds, and finally the A of Spades all the way to the K of Spades. When complete, you will have the entire deck face up, the K of Spades at the top, the A of Hearts at the bottom.
2. Take three cards together as one and lay them down in a pile. Take another three cards together as one and lay them down in another pile. Repeat this two more times until there are four piles of three cards each. Repeat this process until 48 cards have been laid down and each pile has 12 cards each. Then lay the last four cards singly down on the first, second, third, and fourth piles, so there are now 13 cards in each pile.
3. Gather up the piles with the second on top of the first, the third on top of that, and the fourth on top of that.
4. Lay the cards out in four piles again, but THIS time lay them down singly, one on the first pile, on on the second pile, one on the third pile, and one on the fourth pile, repeating this thirteen times until there are again four piles with thirteen cards each.
5. Gather the piles up as before, with the second pile going on the first, the third on top of that, and the fourth on top of that.
This is the entire process. If you started with the order I recommended and have done everything correctly, the first seven cards counting from the top should be the 3 of Hearts, A of Clubs, Q of Clubs, 10 of Spades, 5 of Clubs, 3 of Diamonds, and A of Spades. You'll have to take my word for it that if this process is repeated 90 times, the deck will return to its original order.
Any help whatsoever with this problem will be appreciated, even if it's just to tell me what type of mathematical problem this is, whether a mathematical equation can be produced from this information, or who I meet seek out for help.
Thanks,
Stefan G. Meyer
stefangmeyer@verizon.net
The numerical elements in this problem are quite simple: 52 cards in a deck (Joker is excluded) and 90 times for the procedure. The procedure itself is as follows:
1. The cards are put in a particular order. The order itself is only relevant for the purposes of checking to see if you are doing the operation correctly. To put them in an order that will allow you to easily check, put the cards down face up, starting with the A of Hearts, 2 of Hearts, 3 of Hearts, etc., all the way to the K of Hearts, then followed by the A of Clubs, 2 of Clubs, 3 of Clubs, etc., all the way to the K of Clubs, then the A of Diamonds all the way up to the K of Diamonds, and finally the A of Spades all the way to the K of Spades. When complete, you will have the entire deck face up, the K of Spades at the top, the A of Hearts at the bottom.
2. Take three cards together as one and lay them down in a pile. Take another three cards together as one and lay them down in another pile. Repeat this two more times until there are four piles of three cards each. Repeat this process until 48 cards have been laid down and each pile has 12 cards each. Then lay the last four cards singly down on the first, second, third, and fourth piles, so there are now 13 cards in each pile.
3. Gather up the piles with the second on top of the first, the third on top of that, and the fourth on top of that.
4. Lay the cards out in four piles again, but THIS time lay them down singly, one on the first pile, on on the second pile, one on the third pile, and one on the fourth pile, repeating this thirteen times until there are again four piles with thirteen cards each.
5. Gather the piles up as before, with the second pile going on the first, the third on top of that, and the fourth on top of that.
This is the entire process. If you started with the order I recommended and have done everything correctly, the first seven cards counting from the top should be the 3 of Hearts, A of Clubs, Q of Clubs, 10 of Spades, 5 of Clubs, 3 of Diamonds, and A of Spades. You'll have to take my word for it that if this process is repeated 90 times, the deck will return to its original order.
Any help whatsoever with this problem will be appreciated, even if it's just to tell me what type of mathematical problem this is, whether a mathematical equation can be produced from this information, or who I meet seek out for help.
Thanks,
Stefan G. Meyer
stefangmeyer@verizon.net
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