Not so Intricate..,
Probability
Level
2
The natural numbers are written as a sequence of digits 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22.................. The 2014th digit in the sequence is
8
0
5
7
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1 solution
1, 2, 3, 4, 5, 6, 7, 8, 9 = 9 numbers = 9 digits similarly, 10 to 99 = 90 numbers = 90 x 2 = 180 digits 100 to 999 = 900 numbers = 900 x 3 = 2700 digits
Here, 2014 th digit means, 2014 - (180 + 9) = 1825 digits for which the numbers should be above 99. That means, 1825/3 = 608.33th number after 99. adding the numbers before, 608.33 + (9 + 90) = 707.333
It means, the number will be 707+1 = 708 2014th digit will be the first digit of 708 (because of the 0.333 after 707) hence, the 2014th digit will be 7. :D