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String Theory...not quite (Posted on 2010-07-27) Difficulty: 3 of 5
If the numbers 1 - 100 are written in one long string, how many substrings of minimum length 2 can be found with strictly decreasing numbers? e.g. 12345678910 has three such substrings: 91, 910, 10.

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92 it is! Comment 6 of 6 |

My list of 92 follows.  They are in order of processing: for each start number which begins more than one qualifying substring, I list the 2-number substring, then the 3-number (none larger):

91  910  10  21  31  41  51  61  71  81

92  920  20  21  32  42  52  62  72  82

93  930  30  31  32  43  53  63  73  83

94  940  40  41  42  43  54  64  74  84

95  950  50  51  52  53  54  65  75  85

96  960  60  61  62  63  64  65  76  86

97  970  70  71  72  73  74  75  76  87

98  980  80  81  82  83  84  85  86  87

90   91  92  93  94  95  96  97  98  91

910  10

(Now to see how the humans, elves, and Minotaur getting on -- not my day!)


  Posted by ed bottemiller on 2010-07-27 21:46:46
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