## Count up with Zeckendorf's theorem!

For all your silly time-killing forum games.

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### Re: Count up with Zeckendorf's theorem!

45 = 10010100
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### Re: Count up with Zeckendorf's theorem!

Despite the fact that this system is counter-intuitive for most people, it's regular as hell and hence it's quite easy to see what the successor of any number will be...

46 = 10010101
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### Re: Count up with Zeckendorf's theorem!

46 = 10100000

It is easy to see what the successor would be, but if it weren't a counting game, but a "Find the given number" game, it would be more difficult (without a table containing the Fibonacci series, at least).
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### Re: Count up with Zeckendorf's theorem!

48 = 10100001

What's a "find the given number" game?
Last edited by Sean Quixote on Tue Sep 20, 2011 3:46 am UTC, edited 1 time in total.

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### Re: Count up with Zeckendorf's theorem!

Example: What's x in (given number system, with the rules of the number system explained as necessary.)

48 49 = 10100010

Edit: Oopsie...
Last edited by Anonymously Famous on Tue Sep 20, 2011 3:50 am UTC, edited 1 time in total.
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### Re: Count up with Zeckendorf's theorem!

Oh, so I could say like:

In this number system, you have ones (1s) and zeros (0s). Beginning with "1" and then "10", all subsequent integers must be expressed in a way such that two ones are NEVER adjacent to eachother -- "11" is not ever allowed. Following these rules, how would you express the integer fifty?

50 = 10100100

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### Re: Count up with Zeckendorf's theorem!

51 = 10100101
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### Re: Count up with Zeckendorf's theorem!

52 = 10101000

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### Re: Count up with Zeckendorf's theorem!

53 = 10101001
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### Re: Count up with Zeckendorf's theorem!

54 = 10101010

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### Re: Count up with Zeckendorf's theorem!

55 = 100000000
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### Re: Count up with Zeckendorf's theorem!

56 = 100000001

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### Re: Count up with Zeckendorf's theorem!

57 = 100000010
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### Re: Count up with Zeckendorf's theorem!

58 = 100000100

Sean Quixote

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### Re: Count up with Zeckendorf's theorem!

59 = 100000101
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### Re: Count up with Zeckendorf's theorem!

60 = 100001000

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### Re: Count up with Zeckendorf's theorem!

61 = 100001001
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### Re: Count up with Zeckendorf's theorem!

62 = 100001010

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### Re: Count up with Zeckendorf's theorem!

63 = 100010000
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### Re: Count up with Zeckendorf's theorem!

64 = 100010001

Sean Quixote

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### Re: Count up with Zeckendorf's theorem!

65 = 100010010
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### Re: Count up with Zeckendorf's theorem!

66 = 100010100

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### Re: Count up with Zeckendorf's theorem!

67 = 100010101

a-wan

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### Re: Count up with Zeckendorf's theorem!

68 = 100100000

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### Re: Count up with Zeckendorf's theorem!

69 = 100100001

a-wan

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### Re: Count up with Zeckendorf's theorem!

70 = 100100010

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### Re: Count up with Zeckendorf's theorem!

71 = 100100100

Glad to finally join the fun.

Lorenz

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### Re: Count up with Zeckendorf's theorem!

72 = 100100101

Yaaaay!

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### Re: Count up with Zeckendorf's theorem!

73 = 100101000

Lorenz

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### Re: Count up with Zeckendorf's theorem!

74 = 100101001

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### Re: Count up with Zeckendorf's theorem!

75 = 100101010
Last edited by Lorenz on Wed Sep 28, 2011 5:21 am UTC, edited 1 time in total.

Lorenz

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### Re: Count up with Zeckendorf's theorem!

76 = 101000000

Sean Quixote

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### Re: Count up with Zeckendorf's theorem!

77 = 101000001

Is this truly as easy as it looks?

Lorenz

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### Re: Count up with Zeckendorf's theorem!

78 = 101000010

Yep. The best fractal patterns always are.

Sean Quixote

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### Re: Count up with Zeckendorf's theorem!

79 = 101000100
Obligatory

Lorenz

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### Re: Count up with Zeckendorf's theorem!

79 = 101000100

a-wan

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### Re: Count up with Zeckendorf's theorem!

81 = 101001000

Sean Quixote

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### Re: Count up with Zeckendorf's theorem!

82 = 101001001

The section on using Fibonacci numbers to multiply is awesome.

Lorenz

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### Re: Count up with Zeckendorf's theorem!

83 = 101001010

Sean Quixote

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### Re: Count up with Zeckendorf's theorem!

84 = 101010000

Lorenz

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