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The 5 cards Magic trick Rechallenges! (Posted on 2009-06-01) Difficulty: 4 of 5
In an attempt to solve this problem you have to read "5 Cards Magic Trick" first.

Then here is the Challenge:

Can the "5 Cards Magic Trick" still be performed under the conditions below?

1. The trick is done with 2 mixed packs of cards (meaning, each card appears twice)

2. When the cards are given to Magician B at least one of them must be face down and he mustn't look at it.

Note: the conditions are simultaneous

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Solution No Subject | Comment 1 of 4

A solution quite similar to Daniel's for the original puzzle can be done for this case:

There will be at least one duplication of a suit (hearts, diamonds, clubs or spades), so choose one of the cards of the duplicated suit to give back to C so that B has to guess it.  Make the (or an) other card of the same suit as the first one in the stack for B to see. The one to give back to C should be the one that is "higher" in a circular sense within its suit, that is, like a clock face, where 2 is "higher" than 10 in being clockwise from it via the shortest arc. So far it's the same as Daniel's method.

Now there are three other cards to place in the stack for B to see. In the solution to the former puzzle, the remaining cards were all different, and so all had a different value 1 - 52 preassigned. In the present case, two of the cards may be identical. Since one of the cards must be presented face down, if there are two identical cards, make one of them face down. If all three cards are different, just choose at random one to make face down. Now, instead of the low, middle and high value cards in the old puzzle, you have face-down, lower and higher valued cards.  They can be used in the same manner of six permutations representing numbers 1 - 6, so that you encode with these three cards the number of cards clockwise that you have to go to get from the first card in the stack to the value of the hidden card of the same suit.

One small deviation from the above: If the only two cards of the same suit are in fact identical, so the clockwise distance is zero, do not use the card identical to the card returned to C as the first card; use some other one, regardless of suit. Make whatever card you put first the one that's upside down. The next card should then be the one identical to the card returned to C so that B can see that when the first card is the downturned one, then the next one is identical to the card to be guessed.

  Posted by Charlie on 2009-06-01 14:15:02
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