Card Tricks > Contest Card Tricks
Third Color Theme
Is a game played by three spectators with the performer acting the
part of the referee. Since the contest calls for some very logical
reasoning on the part of the participants, it should be reserved for
presentation only to people who have the intelligence to recognise and
appreciate both the challenge offered by the contest and the neatness of
the ultimate solution.
Presentation
The performer seats three contestants triangular wise around a table
facing the table center. Three books are placed in an upright position
directly in front of each spectator. These books are deliberately
positioned so that although each contestant can see what is the back of
the two books, he is unable to see what is back of his own book.
The contestants are then told that a single playing card, either red or
black, is to be placed face outward behind each of the three books. They
will be placed so that each contestants can see the color of the other
two contestants' cards but not his own. Of the three cards, at least one
must be red. Each contestant has to identify the color of the card he
cannot see. With this explanatory preamble, the performer proceeds to
secretly select the three red cards from the pack and place one each
behind each book. From the given card arrangement each contestant must
now proceed to deduce the color of his own card. The spectator who first
announces his card color wins.
Method
This trick necessarily calls for the selection of three fairly
intelligent spectators, since a certain degree of intuitive reasoning is
required to arrive at an answer to this problem in logic.
Consider first the case where the performer might have distributed one
red and two black cards. Under these conditions, one of the contestants
would immediately have seen two black cards and knowing that at least
one of the three cards is red, would correctly announce that his must be
the red card.
Consider next the case where the performer distributes one black and two
red cards. Observing this situation, it will not be too long before one
of these two contestants (say A) will reason that if his card were also
black, two black cards would be immediately visible to the third
contestant (say C). In this condition, C would announce his card as red.
Since the third contestant C fails to announce immediately this fact,
contestant A can be reasonably assured that his own card cannot be
black. Therefore it must be red.
Comment
The logical solution given under the actual method is an elegant bit
of deduction. However, for the record, it should be noted that a less
rigorous alternate solution is also possible. Thus in being strictly
fair to all three contestants, it could be argued than an equal set of
conditions would be required . Obviously, this could only be done by a
symmetrical
three red card distribution. However, although this is an ethnical
approach to the solution, it lacks the neatness of the theoretical
deduction.
Card Tricks > Contest Card Tricks
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