Download - Magical Mathematics! Mathematics! David Lipshutz Vartan Gregorian Science Conference June 11, 2014
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Magical Mathematics!David Lipshutz
Vartan Gregorian Science Conference
June 11, 2014
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Cutting the deck keeps the order
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Cutting the deck keeps the order
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Cutting the deck keeps the order
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Cutting the deck keeps the order
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Cutting the deck keeps the order
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Cutting the deck keeps the order
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Cutting the deck keeps the order
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Cut the deck
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1
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Draw two cards
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Ask what color they are
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Match the colors
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Match the colors
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1
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Match the colors
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Match the colors
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Match the colors
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Order is important!
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1. Black Black
Order is important!
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1. Black Black2. Red Black
Order is important!
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1. Black Black2. Red Black3. Red Red
Order is important!
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1. Black Black2. Red Black3. Red Red4. Black Red
Order is important!
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1. Black Black2. Red Black3. Red Red4. Black Red
Order is important!
Every combination only happens once!
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Order is important!1
2
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Order is important!
1. Red Black
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Order is important!
1. Red Black2. Black Red
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Order is important!
1. Red Black2. Black Red3. Red Black
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Order is important!
1. Red Black2. Black Red3. Red Black4. Black Red
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Order is important!
1. Red Black2. Black Red3. Red Black4. Black Red
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Combinations repeat!
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Order is important!
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Order is important!
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Order is important!
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Order is important!
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1
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Order is important!
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1
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Order is important!
Uh oh :(
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What’s special about the order?
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What’s special about the order?
Every color combination only happens once!
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What’s special about the order?
Every color combination only happens once!
Can we do this trick with more cards?
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What’s special about the order?
Every color combination only happens once!
Can we do this trick with more cards?
Yes, but we need longer combinations!
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The Magic of de Bruijn Sequences
BBRR
Deck of 4 cards: 2 card combinations
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The Magic of de Bruijn Sequences
BBRR
Deck of 4 cards: 2 card combinations
Deck of 8 cards: 3 card combinations
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The Magic of de Bruijn Sequences
BBRR
BBBRRRBR
Deck of 4 cards: 2 card combinations
Deck of 8 cards: 3 card combinations
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The Magic of de Bruijn Sequences
BBRR
BBBRRRBR
Deck of 4 cards: 2 card combinations
Deck of 8 cards: 3 card combinations
Deck of 16 cards: 4 card combinations
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The Magic of de Bruijn Sequences
BBRR
BBBRRRBR
BBBBRBRRRRBBRRBR
Deck of 4 cards: 2 card combinations
Deck of 8 cards: 3 card combinations
Deck of 16 cards: 4 card combinations
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Deck of 32 cards: 5 card combinations
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Deck of 32 cards: 5 card combinations
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Deck of 32 cards: 5 card combinations
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1 2 34
5
Deck of 32 cards: 5 card combinations
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1 2 34
5
Deck of 32 cards: 5 card combinations
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1 2 34
5
1 2 34
5
Deck of 32 cards: 5 card combinations
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1 2 34
5
1 2 34
5
Deck of 32 cards: 5 card combinations
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Secret codes
Robot vision
Reading DNA
The Magic of de Bruijn Sequences
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Magical Mathematics!
Persi Diaconis Ron Graham