QUESTION

CSAT

Hard

Maths

Prelims 2025

What is the 489th digit in the number 123456789101112...?123456789101112...?

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Explanation

Count digits in blocks:

  • 1-digit numbers (1–9): 9 digits total.
  • 2-digit numbers (10–99): 90 numbers ×\times 2 = 180 digits.

Cumulative after 1- and 2-digit numbers: 9 + 180 = 189 digits.

We want the 489th digit \rightarrow remaining after 189 = 489 - 189 = 300 digits, which come from 3-digit numbers (each contributes 3 digits).

Number of 3-digit numbers needed: 300 ÷\div 3 = 100 numbers \rightarrow 100 to 199.

Thus, the 489th digit is the last digit of 199, which is 9\textbf{9}.

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