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 2000 cards (Posted on 2009-01-04)
There are cards labeled from 1 to 2000. The cards are arranged and placed in a pile.

The top card is placed on the table, then the next card at the bottom of the pile.

Then the next card is placed on the table to the right of the first card, and the next card is placed at the bottom of the pile.

This process is continued until all the cards are on the table.

The final order (from left to right) is 1, 2, 3, ... , 2000.

In the original pile, how many cards were above card labeled 1999?

 See The Solution Submitted by pcbouhid No Rating

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 re(2): computer solution (spoiler) | Comment 6 of 9 |
(In reply to re: computer solution (spoiler) by elementofsurprize)

I see what happened in your calculations.  When you cycle to the top of the deck, your calculations always take the first card available in the whole deck; but that fails to skip a card in some instances. I've recalculated the numbers in a way that matches yours, and note that the first divergence is after placing the originally 2000th card onto the 1938th position on the table. Your calculation places the originally 32nd card next.  But that's the very next card; you haven't skipped one.  There's no demarcation given at the top of the deck to indicate you should start over, as the old cards were just placed at the bottom, so in the actual physical embodyment, there's no warning to start fresh and disregard the fact that you're not skipping over a card.

After placing card 2000 into position 1938, card 32 should be skipped over and card 64 placed into position 1939.

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 Posted by Charlie on 2009-01-05 10:05:50

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