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The digit in question is 1.
First, we need to realize that the first 9 one-digit numbrs provide 9 digits. 180 digits come from the 90 two-digits numbers, 2700 digits come from the 900 three-digit numbers, and so on. The set of n-digit numbers will provide 9n×10^n digits to the list.
Based on this, we get:
Digits 1-9 come from the 1-digit numbers.
Digits 10-189 come from the 2-digit numbers.
Digits 190-2889 come from the 3-digit numbers.
Digits 2890-38889 come from the 4-digit numbers.
Digits 38890-488889 come from the 5-digit numbers.
So, the 40000th digit must be the 1111th digit of the sequence of 5 digit numbers.
We also know that 1111=222×5+1, so the 1111th digit of this set is the first digit of the 223rd 5-digit number.
10222 is the 223rd 5 digit number, which means that 1 is the 40000th digit of the overall sequence. |
