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Fibonacci Solitaire. Cliff F. Smith June 8, 2010 Presented in partial fulfillment of the requirements for the MST in mathematics. Example Game. Example Game. Example Game. Example Game. Example Game. Example Game. Example Game. Example Game. Example Game. Example Game. Removed Pairs.
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Fibonacci Solitaire Cliff F. Smith June 8, 2010 Presented in partial fulfillment of the requirements for the MST in mathematics
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Example Game Removed Pairs
Game Over Removed Pairs
Game Over Removed Pairs We Lose
Notation Removed Pairs
Notation 8 (6,5) (7,1) (4,3) 2
Notation (6,5) (7,1) (4,3) 2 8
Notation (6,5) (7,1) (4,3) 2 8 • Write pairs with the smaller card first
Notation (6,5) (7,1) (4,3) 2 8 • Write pairs with the smaller card first
Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first
Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first
Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first • Organize numerically
Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first • Organize numerically • (by singles and smaller card in pairs)
Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first • Organize numerically • (by singles and smaller card in pairs)
Notation (1,7) 2 (3,4) 8 (5,6) • Write pairs with the smaller card first • Organize numerically • (by singles and smaller card in pairs)
Notation (1,7) 2 (3,4) 8 (5,6) • Write pairs with the smaller card first • Organize numerically • (by singles and smaller card in pairs)
Notation (1,7) 2 (3,4) (5,6) 8 • Write pairs with the smaller card first • Organize numerically • (by singles and smaller card in pairs)
Notation (1,7) 2 (3,4) (5,6) 8 • Write pairs with the smaller card first • Organize numerically • (by singles and smaller card in pairs)
Play! • Keep track of initial order of cards
Play! • Keep track of initial order of cards • Write final set of pairs and singles in correct notation
Some Questions • What is the probability of winning?
Some Questions • What is the probability of winning? • Hard to answer
Some Questions • What is the probability of winning? • Hard to answer • 2. Is the Fibonacci solitaire algorithm a function?
Some Questions • What is the probability of winning? • Hard to answer • Is the Fibonacci solitaire algorithm a function? • Yes
(1,7) 2 (3,4) (5,6) 8 More Notation
(1,7) 2 (3,4) (5,6) 8 More Notation FS(8, 5, 3, 4, 1, 7, 6, 2) = (1,7) 2 (3,4) (5,6) 8
The Function FS Orderings of a deck of cards. (permutations) Pairings (partial and total)
Some Questions • What is the probability of winning? • Hard to answer • Is the Fibonacci solitaire algorithm a function? • Yes • 3. Is the FS function injective?