Riya's birthday falls on Sunday, 4th June. On what day of the week will…

Concept: In calendar problems, the day of the week for a target date is found by counting the total number of days elapsed from a date whose day is already known, then dividing that count by 7 — the remainder is the number of days to advance from the known day, since the 7-day week cycle repeats exactly every 7 days.

Application:

1. Days remaining in June from the 4th (30 minus 4): 26 days.

2. Full month of July: 31 days.

3. Full month of August: 31 days.

4. Full month of September: 30 days.

5. Full month of October: 31 days.

6. Days elapsed into November up to the 2nd: 2 days.

7. Total days elapsed = 26 + 31 + 31 + 30 + 31 + 2 = 151 days.

8. 151 divided by 7 = 21 remainder 4 (since 21 × 7 = 147).

9. A remainder of 4 means the day of the week advances 4 days from Sunday: Monday (1), Tuesday (2), Wednesday (3), Thursday (4).

Cross-check: Assigning Sunday = 0, Monday = 1, Tuesday = 2, Wednesday = 3, Thursday = 4 in the weekly cycle, a remainder of 4 maps directly onto Thursday, confirming the result independently of the running-sum method above.

Hence, Prisha's birthday falls on Thursday.