1. **Stating the problem:** We are given the days of the week for certain dates in 2025 and asked to verify if the given statements about dates in 2026 are true or false. Given: - 17 May 2025 is Saturday - 10 July 2025 is Thursday - 2 September 2025 is Tuesday Statements to verify: - 1 January 2026 is Wednesday - 5 March 2026 is Thursday - 17 April 2026 is Friday 2. **Formula and rules:** To find the day of the week for a given date, we can use the fact that each year advances the day of the week by 1 day if it is a common year, or 2 days if it is a leap year. 2025 is not a leap year (divisible by 4? No), so 2026 is also not a leap year. 3. **Calculate day of week for 1 January 2026:** - From 17 May 2025 (Saturday) to 1 January 2026: Count days from 17 May 2025 to 31 December 2025. Days in each month after May 17: - May: 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 4. **Calculate day of week shift:** - Number of weeks in 228 days = $\frac{228}{7} = 32$ weeks and 4 days remainder. - So, day of week advances by 4 days from Saturday. 5. **Find day of week for 1 January 2026:** - Saturday + 4 days = Wednesday So, 1 January 2026 is Wednesday. Statement is **Yes**. 6. **Calculate day of week for 5 March 2026:** - From 1 January 2026 (Wednesday) to 5 March 2026: Days in January after 1st: 31 - 1 = 30 days Days in February 2026: 28 days (not leap year) Days in March before 5th: 4 days Total days = 30 + 28 + 4 = 62 days 7. **Calculate day of week shift:** - $\frac{62}{7} = 8$ weeks and 6 days remainder - Day advances by 6 days from Wednesday 8. **Find day of week for 5 March 2026:** - Wednesday + 6 days = Tuesday Statement says Thursday, so this is **No**. 9. **Calculate day of week for 17 April 2026:** - From 5 March 2026 (Tuesday) to 17 April 2026: Days in March after 5th: 31 - 5 = 26 days Days in April before 17th: 16 days Total days = 26 + 16 = 42 days 10. **Calculate day of week shift:** - $\frac{42}{7} = 6$ weeks and 0 days remainder - Day advances by 0 days from Tuesday 11. **Find day of week for 17 April 2026:** - Tuesday + 0 days = Tuesday Statement says Friday, so this is **No**. **Final answers:** - 1 January 2026 is Wednesday: ✓ Yes - 5 March 2026 is Thursday: ✗ No - 17 April 2026 is Friday: ✗ No