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Previous Year Question (PYQs)

Consider a sequence formed by concatenating the positive integers in increasing order: 12345678910111213 ... Which among the following is the closest to the 2028th digit in this infinite sequence?




Solution

1-digit numbers: 1 to 9 → 9 digits
2-digit numbers: 10 to 99 → 90 × 2 = 180 digits
Total till 99 → 9 + 180 = 189 digits
Remaining → 2028 − 189 = 1839 digits (in 3-digit range)
Each 3-digit number has 3 digits → 1839 ÷ 3 = 613 numbers (approx.)
Last full number before 2028th digit → 100 + 612 = 712
712 → digits are 7, 1, 2
Hence, the 2028th digit = 2

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