How must a deck of red and black cards be ordered so that, dealing the top card face up and putting the...

magic/card/alternating.colors New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

How must a deck of red and black cards be ordered so that, dealing the
top card face up and putting the next one under the deck, over and
over, the cards turn up black, red, black, red, ...?

>How about the following: you take a number of cards, half of them
>black and half of them red.  E.g 7 red and 7 black.  You put them in
>some order.
>
>Then you take the first card (the one on top) out of the deck, let
>everyone see it: it is black.
>The next card you will place under the deck.
>Then take the third card: it's red.
>The 4'th card goes under the deck.
>
>You keep on repeating this until the deck is empty.  Everyone will
>see: black, red, black, red, etc.
>Now you give the cards to someone else and say: do the same.

-- Mark van Hoeij <hoeij@sci.kun.nl>, "Thinking Backwards", September
   1993

Show solution

The order of the cards should be:

B B R R B R R R B B R B
  |   |   |   |   |   |
  Those cards go to the end and  then you have on the second "turn":
  B B R R R B
  |   |   |
  And then those go to the end and you have
  R R B
    |
    And this one goes to the end.

You can check it: the unmarked cards are in the right order.

-- Livian Segal <jhsegal@wiscon.weizmann.ac.il>

[ Editor: the order uses 6 red and 6 black cards.  The cards marked |
in the first line (the 2nd, 4th, ..., 12th) are B R R R B B, not
B B R R R B as in the second line; with B R R R B B the second turn
shows B, R, B and leaves R R B, as in the third line. ]