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 Monotonous integers (Posted on 2015-12-30)
For how many integers having between 1 and 10 digits (base 10) are all of their digits when read from left to right monotonically increasing? In other words, every digit is less than or equal to all of those to its right. For example, 244467889 is one of them, and 0 is another, but there are more.

 See The Solution Submitted by Steve Herman Rating: 1.0000 (1 votes)

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 found the mapping | Comment 5 of 9 |

@ Jer:   The sum for C(8+m,8) equals  for (m from 0 to m)
C(9+m,m).

For m=10 equals C(19,9)
i.e, 92,378

I have found the  1 to 1 mapping of all 10 digit  numbers from 0 to 9,999,999,9999  into a binary string of 19 bits;( 10 zeroes and 9 ones.)

After 2 days of  "suffering", I have on my hands a 10 minute solution, will describe later.

Edited on December 31, 2015, 3:26 am
 Posted by Ady TZIDON on 2015-12-31 02:56:33

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