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Fibonacci Solitaire

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

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  1. Fibonacci Solitaire Cliff F. Smith June 8, 2010 Presented in partial fulfillment of the requirements for the MST in mathematics

  2. Example Game

  3. Example Game

  4. Example Game

  5. Example Game

  6. Example Game

  7. Example Game

  8. Example Game

  9. Example Game

  10. Example Game

  11. Example Game Removed Pairs

  12. Example Game Removed Pairs

  13. Example Game Removed Pairs

  14. Example Game Removed Pairs

  15. Example Game Removed Pairs

  16. Example Game Removed Pairs

  17. Example Game Removed Pairs

  18. Example Game Removed Pairs

  19. Example Game Removed Pairs

  20. Example Game Removed Pairs

  21. Example Game Removed Pairs

  22. Game Over Removed Pairs

  23. Game Over Removed Pairs We Lose 

  24. Notation Removed Pairs

  25. Notation

  26. Notation 8 (6,5) (7,1) (4,3) 2

  27. Notation (6,5) (7,1) (4,3) 2 8

  28. Notation (6,5) (7,1) (4,3) 2 8 • Write pairs with the smaller card first

  29. Notation (6,5) (7,1) (4,3) 2 8 • Write pairs with the smaller card first

  30. Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first

  31. Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first

  32. Notation (5,6) (1,7) (3,4) 2 8 • Write pairs with the smaller card first • Organize numerically

  33. 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)

  34. 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)

  35. 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)

  36. 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)

  37. 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)

  38. 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)

  39. Play!

  40. Play! • Keep track of initial order of cards

  41. Play! • Keep track of initial order of cards • Write final set of pairs and singles in correct notation

  42. Some Questions

  43. Some Questions • What is the probability of winning?

  44. Some Questions • What is the probability of winning? • Hard to answer

  45. Some Questions • What is the probability of winning? • Hard to answer • 2. Is the Fibonacci solitaire algorithm a function?

  46. Some Questions • What is the probability of winning? • Hard to answer • Is the Fibonacci solitaire algorithm a function? • Yes

  47. (1,7) 2 (3,4) (5,6) 8 More Notation

  48. (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

  49. The Function FS Orderings of a deck of cards. (permutations) Pairings (partial and total)

  50. 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?

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