By Sir James George Frazer
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Additional info for The Golden Bough Part 1 The Magic Art and the Evolution of Kings
At this point, there is a pile of face-up/face-down cards on the table. ” The spectator gets one more decision—after the performer deals the cards into two piles (left, right, left, right, and so on) the spectator chooses a pile, turns it over, and puts it on top of the other pile. For the denouement, the performer explains that the highest hand in poker, the perfect poker hand, is a royal flush—ace, king, queen, jack, and ten, all of the same suit. The cards are spread and there are exactly five face-down cards.
If yes, you are home. If no, you are home as well. Throughout this book we go from magic to mathematics, and back. We have just posed a math problem arising from a magic trick: Is there a neat way to arrange a deck of fifty-two cards that does what is needed? We leave this to the interested reader. Chapter 3 IS THIS STUFF ACTUALLY GOOD FOR ANYTHING? , go through each of the successive sixteen zero/one strings of length four once (going around the corner). Such a sequence is called a de Bruijn sequence of window length four.
This has the effect of forcing the chosen card to be the oddball. Again, two cases to check. End of story. , 2n, after an arbitrary number of Hummer shuffles. The following theorem delineates exactly what can happen. THEOREM. After any number of Hummer shuffles of 2n cards, any arrangement of values is possible. However, the face-up/facedown pattern is constrained as follows: Consider the card at position i. Add one to its value if face-up. Add this to i. This sum is simultaneously even (or odd) for all positions i.