Microsoft PowerPoint slides92
Short summary:
Magic Trick Revealed (II). How do we figure out the value of. the hidden card? ... The Magic Trick. 1. The audience chooses 5 cards. from a shuffled deck. ...
Long summary:
Microsoft PowerPoint slides92Page 11Mathematics for Computer Science MIT 6.042J/18.062J Combinatorics II.2 Copyright 2002 by Radhika Nagpal and Charles E. Leiserson. L92.1 What Can the Assistant Do? Decide in which order to reveal the cards: 4 cards 4! orders = 24 orders. Decide which 4 cards to reveal: 5 ways to choose which card to hide. Copyright 2002 by Radhika Nagpal and Charles E. Leiserson. L92.3 Magic Trick Revealed (II) How do we figure out the value ofthe hidden card? Aha! ok at the order of the other 3 cards! Aha! ok at the order of the other 3 cards! LoLoA < 2 < 3 < L < KTotal order < A < 2 < 3 < L < Kon the cards < A < 2 < 3 < L < K< A < 2 < 3 < L < KCopyright 2002 by Radhika Nagpal and Charles E. Leiserson. L92.5 The Magic Trick 1. The audience chooses 5 cards from a shuffled deck. 2. The assistant reveals 4 cards. 3. The magician correctly guessesthe 5th card. Q. What is the role of the assistant? Copyright 2002 by Radhika Nagpal and Charles E. Leiserson. L92.2 Magic Trick Revealed (I) The audience picks 5 cards: At least 2 cards must have the same suit (Pigeonhole Principle). Aha! same suit as the hidden card! Aha! same suit as the hidden card!The first card has the The first card has the Copyright 2002 by Radhika Nagpal and Charles E. Leiserson. L92.4 Magic Trick Revealed (II) How do we figure out the value ofthe hidden card? Aha! ok at the order of the other 3 cards! Aha! ok at the order of the other 3 cards! LoLoA < A < A < AAnother < 2 < 2 < 2 < 2possible Morder < K < K < K < KCopyright 2002 by Radhika Nagpal and Charles E. Leiserson. L92.6 Page 22L92.8Copyright 2002 by Radhika Nagpal and Charles E. Leiserson. Clockwise Distance 58 AQ 67 K 2J 310 49 Between any 2 of the 13 values the smaller clockwise distance is at most 6: 7 6 Hide the card with the smaller offset. Magic Trick Revealed (III) But wait! There are 12 possible values forthe h ...
Source: ocw.mit.edu
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