A simple card trick? The magician has a spectator choose a card, memorize it, and return it to the top of the deck. She then allows the spectator to cut the cards-split the deck into two by taking a set of cards from the top, and then switch the two parts-as many times as he would like. The magician spreads the cards face up and .. . announces the chosen card. Analyze and explain the above trick using the following steps: Step 1: Consider a deck of 52 cards C1, C2,..., C52, and let H be the subgroup of S52 generated by (1 2 o. C; = Co(i). Show that this gives an action of H on the deck of cards. Step 2: LetT = C52. Now, if we apply T to the deck of cards, then what happens to the order of the cards? What if we apply 72? Show that any “cutting of the cards" can be achieved by the action of an element of H. Step 3: Let N = {{C1, C2}, {C2, C3}, ...,{C52,C1}} be the set of consec- utive pairs of cards in the original deck. Show that the action of H on the deck of cards results in an action of H on N. Conclude that cutting the deck does not change the set of consecutive pairs of cards. Step 4: Explain the card trick. 51 52). If o E H, then define ... (1 2 51 52), and put the deck in the order C1, C2, ...,
A simple card trick? The magician has a spectator choose a card, memorize it, and return it to the top of the deck. She then allows the spectator to cut the cards-split the deck into two by taking a set of cards from the top, and then switch the two parts-as many times as he would like. The magician spreads the cards face up and .. . announces the chosen card. Analyze and explain the above trick using the following steps: Step 1: Consider a deck of 52 cards C1, C2,..., C52, and let H be the subgroup of S52 generated by (1 2 o. C; = Co(i). Show that this gives an action of H on the deck of cards. Step 2: LetT = C52. Now, if we apply T to the deck of cards, then what happens to the order of the cards? What if we apply 72? Show that any “cutting of the cards" can be achieved by the action of an element of H. Step 3: Let N = {{C1, C2}, {C2, C3}, ...,{C52,C1}} be the set of consec- utive pairs of cards in the original deck. Show that the action of H on the deck of cards results in an action of H on N. Conclude that cutting the deck does not change the set of consecutive pairs of cards. Step 4: Explain the card trick. 51 52). If o E H, then define ... (1 2 51 52), and put the deck in the order C1, C2, ...,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A simple card trick?
The magician has a spectator choose a card, memorize it, and
return it to the top of the deck. She then allows the spectator
to cut the cards split the deck into two by taking a set of cards
from the top, and then switch the two parts-as many times
as he would like. The magician spreads the cards face up and
announces the chosen card.
Analyze and explain the above trick using the following steps:
Step 1: Consider a deck of 52 cards C1, C2,..., C52, and let H be the
subgroup of S32 generated by (1 2
o . C; = C,(i): Show that this gives an action of H on the deck of cards.
Step 2: Let T =
C52. Now, if we apply T to the deck of cards, then what happens to the
order of the cards? What if we apply r2? Show that any "cutting of the
cards" can be achieved by the action of an element of H.
Step 3: Let N = {{C1, C2}, {C2, C3}, ... , {C52, C1}} be the set of consec-
utive pairs of cards in the original deck. Show that the action of H on
the deck of cards results in an action of H on N. Conclude that cutting
the deck does not change the set of consecutive pairs of cards.
Step 4: Explain the card trick.
51 52). If o E H, then define
...
(1 2
51 52), and put the deck in the order C1, C2, ...,
..
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