Which day is 10th October, 2027?

To determine the day of the week for October 10, 2027, we can use the concept of odd days. 1. **Find the day for January 1, 2027:** * We know January 1, 2024, was a Monday. * From Jan 1, 2024, to Jan 1, 2025: 2024 is a leap year (366 days = 52 weeks + 2 odd days). So, Jan 1, 2025 = Monday + 2 days = Wednesday. * From Jan 1, 2025, to Jan 1, 2026: 2025 is a common year (365 days = 52 weeks + 1 odd day). So, Jan 1, 2026 = Wednesday + 1 day = Thursday. * From Jan 1, 2026, to Jan 1, 2027: 2026 is a common year (365 days = 52 weeks + 1 odd day). So, Jan 1, 2027 = Thursday + 1 day = Friday. 2. **Calculate odd days from January 1, 2027, to October 10, 2027:** * January (remaining 30 days from Jan 2 to Jan 31): 30 mod 7 = 2 odd days * February (2027 is not a leap year, 28 days): 28 mod 7 = 0 odd days * March (31 days): 31 mod 7 = 3 odd days * April (30 days): 30 mod 7 = 2 odd days * May (31 days): 31 mod 7 = 3 odd days * June (30 days): 30 mod 7 = 2 odd days * July (31 days): 31 mod 7 = 3 odd days * August (31 days): 31 mod 7 = 3 odd days * September (30 days): 30 mod 7 = 2 odd days * October (first 10 days): 10 mod 7 = 3 odd days Total odd days = 2 + 0 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 = 23 odd days. Now, find the remainder when 23 is divided by 7: 23 mod 7 = 2. 3. **Add the odd days to the reference day:** Starting from Friday (Jan 1, 2027) + 2 odd days = Sunday. Therefore, October 10, 2027, will be a Sunday. The final answer is A) Sunday.