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Problem
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Many thanks to Sudipta Das for the suggestion that lead to this problem.
Please note that, due to an editing error on my part left, I left off the (crucial) third condition. My apologies....
Place the playing cards 2, 3, 4, 5, 6 in a row. How many moves does it take to reverse the order of the cards using only moves of the following kind?
· A card can be slid to fill a space to its right or left.For example, a 2 can be placed on a 3, but a 4 cannot be placed on a 2. You may assume that at the start there are infinitely many free space to the left and to the right of the row of cards.
· A card of lower value can be place on one of higher value, but not the other way around.
· No blank spaces are allowed between cards
(In the case of only the cards 2, 3, 4, the following
solution is minimal. (R = move right, L = move left)
2: RRR; 3: R; 2: LL; 3: R; 2: RRR. )
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For the less inhibited: How many moves are required for n
cards -- maybe an upper bound and a lower bound that are close?
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ã2002 Alberto L. Delgado