The Champernowne word 1234567891011121314151617181920212223... is an infinitely long string of digits made up of all positive integers written in ascending order without any separators between the individual numbers. This function should return the integer digit that lies in the position n of the Champernowne word, position count again starting from zero as usual.
Up for the count
def counting_series(n):
The Champernowne word 1234567891011121314151617181920212223... is an infinitely long string of digits made up of all positive integers written in ascending order without any separators between the individual numbers. This function should return the integer digit that lies in the position n of the Champernowne word, position count again starting from zero as usual.
Of course, the automated tester will give your function values of n large enough that anybody trying to solve this problem by explicitly constructing the series as a string would run out of time and space long before receiving the answer. Instead, you should observe that the structure of this infinite sequence is quite straightforward, as it starts with 9 single-digit numbers, followed by 90 two-digit numbers, followed by 900 three-digit numbers, and so on. Such a predictably self-similar structure allows you to skip over prefixes of this series in exponentially widening leaps and bounds, until you reach the position n and find out the digit that is waiting for you there.
Out of curiosity, has the digit that was waiting for you in position n been waiting for you there since the dawn of time? Or did the answer come to existence the moment that somebody first posed this problem, or only when somebody actually solved this problem up to the position n? What is your stance on this thorny and ancient philosophical issue that is well above this author's pay grade? Do all mathematical structures and the answers to all possible questions about these structures already exist in the static and timeless Platonic plane of perfect forms for us to discover by means of reason?
Or are at least some mathematical truths lazily created by social agreement as the need for them
emerges, so that their existence is similar to that of fictional characters such as Donald Duck and
James Bond, woven into our reality by the arbitrary decisions of their creators?
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