1. **Stating the problem:** We are given the days of the week for certain dates in 2025 and asked to determine the days of the week for specific dates in 2026. 2. **Given information:** - 17 May 2025 is Saturday - 10 July 2025 is Thursday - 2 September 2025 is Tuesday 3. **Goal:** Determine the day of the week for: - 1 January 2026 - 5 March 2026 - 17 April 2026 4. **Important rules:** - 2025 is not a leap year (since 2024 is leap, 2025 is common year with 365 days). - Days of the week advance by 1 day each year plus 1 extra day if there is a leap year in between. - To find the day of the week for a date, count the number of days difference from a known date and use modulo 7. 5. **Step 1: Find day of 1 January 2026** - From 17 May 2025 (Saturday) to 1 January 2026: - Calculate days from 17 May 2025 to 31 December 2025. - May 17 to May 31: $31 - 17 = 14$ days - June: 30 days - July: 31 days - August: 31 days - September: 30 days - October: 31 days - November: 30 days - December: 31 days Total days = $14 + 30 + 31 + 31 + 30 + 31 + 30 + 31 = 228$ days - Days modulo 7: $228 \mod 7 = 4$ (since $7 \times 32 = 224$, remainder 4) - Day of week advances by 4 days from Saturday: Saturday (6), Sunday (0), Monday (1), Tuesday (2), Wednesday (3), Thursday (4), Friday (5) Counting: Saturday +1=Sunday, +2=Monday, +3=Tuesday, +4=Wednesday So 1 January 2026 is Wednesday. 6. **Step 2: Find day of 5 March 2026** - From 1 January 2026 (Wednesday) to 5 March 2026: - January: 31 days - February 2026 (not leap year): 28 days - March 1 to March 5: 5 days Total days = $31 + 28 + 5 = 64$ days - Days modulo 7: $64 \mod 7 = 1$ (since $7 \times 9 = 63$, remainder 1) - Day advances by 1 day from Wednesday: Wednesday +1 = Thursday So 5 March 2026 is Thursday. 7. **Step 3: Find day of 17 April 2026** - From 5 March 2026 (Thursday) to 17 April 2026: - March 6 to March 31: $31 - 5 = 26$ days - April 1 to April 17: 17 days Total days = $26 + 17 = 43$ days - Days modulo 7: $43 \mod 7 = 1$ (since $7 \times 6 = 42$, remainder 1) - Day advances by 1 day from Thursday: Thursday +1 = Friday So 17 April 2026 is Friday. 8. **Final answers:** - 1 January 2026 is Wednesday (Ya) - 5 March 2026 is Thursday (Ya) - 17 April 2026 is Friday (Ya)