Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?
Answer & explanation
Answer: (c) 81
111111111 × 111111111 = 12345678987654321. Its digits add up to 2 × (1 + 2 + … + 8) + 9 = 72 + 9 = 81.
- Pattern: 11² = 121, 111² = 12321, 1111² = 1234321, and so on.
- So 111111111² = 12345678987654321.
- Digit sum = 2 × (1 + 2 + … + 8) + 9 = 2 × 36 + 9 = 81.
- Check: with n ones the digit sum of the square is n², and 9² = 81.
Remember · Squares of numbers made of n ones (n up to 9) are palindromes 123…n…321 with digit sum n².
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·