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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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Solution solution | Comment 2 of 6 |
There are 92 substrings where the substring may represent a number of decending digits. Of these, there are 53 numbers with decending digits represented.

 10,  20,  21,  30,  31,  32,  40,  41,  42,  43,
 50,  51,  52,  53,  54,  60,  61,  62,  63,  64,
 65,  70,  71,  72,  73,  74,  75,  76,  80,  81,
 82,  83,  84,  85,  86,  87,  90,  91,  92,  93,
 94,  95,  96,  97,  98, 910, 920, 930, 940, 950,
960, 970, 980

All the numbers but those ending in the digit 0 are repeated twice, with the exceptions that 91 is repeated thrice, and 10 and 910 twice:
... 8 9 10 11 ... 89 99 100.
... 8 9 10 11 ... 90 91 92 ... 89 99 100.
... 8 9 10 11 ... 89 99 100.

Edited on July 27, 2010, 7:18 pm
  Posted by Dej Mar on 2010-07-27 13:21:29

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