Where are they hiding ?
Number Theory
Level
3
\[ 012345678910{\color{blue}111}21314\ldots\]
The above is the beginning of all non-negative integers concatenated into a single infinite string.
\(\color{blue}111\) is the first sub-string with 3 identical digits in a row, with different digits preceding and following the run of the identical digits. The first \(\color{blue}1\) of \(\color{blue}111\) comes at position 13 (from left) in the infinite string.
Where is the first such sub-string with 4 identical digits?
Give the position of the first digit of the four.
by
Romain Bouchard