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UPSC CSE 2025 · PYQ · Number Sequences · medium

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

  1. A.0
  2. B.3
  3. C.6✓ Correct
  4. D.9

Explanation

Digits 1-9 take positions 1-9 (9 digits). Two-digit numbers 10-99 take 90 × 2 = 180 digits, occupying positions 10 to 189. Three-digit numbers start from position 190. Position 489 is within three-digit numbers. Digits remaining after position 189: 489 − 189 = 300. Each three-digit number takes 3 digits, so 300/3 = 100 complete three-digit numbers. The 100th three-digit number is 100 + 99 = 199. So position 489 is the last (3rd) digit of 199, which is 9. Wait, reconsider: positions 190-192 are 100, 193-195 are 101, ..., the kth three-digit number occupies positions 190+3(k-1) to 192+3(k-1). For k=100: positions 487, 488, 489 correspond to the number 199. So position 489 is the last digit of 199 = 9. Hmm, but option (c) 6 may be the official. Let me recheck: 489-189=300, 300÷3=100 exactly, so the 100th three-digit number (which is 199) ends at position 489. The digit is 9. Answer (d) 9.
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