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The counting numbers are written one after another without any spaces: 1234567891011121314151617181920… . What digit is in the 2020th position?

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5 votes

Answer:

7

Explanation:

One-digit and two-digit numbers occupy 9 + 2*90 = 189 positions.

The amount of the rest positions from 190-th till 2020-th is 2020 - 189 = 1831.

The number of the three-digit numbers occupying these 1831 positions is 1831%2F3 = 610.33.

It means that the positions from 190 till 2019 are occupied by the three-digit numbers

100, 101, 102, . . . , 100+610-1 = 709.

Hence, the digit in 2020 position is "7", the first digit of the number 710

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