Monday falls on 4th April, 1988. What was the day on 3rd November, 1987?

In calendar problems, once the day of week for one date is known, the day for any other date is found by counting the total number of days between the two dates and reducing that count modulo 7 — the calendar repeats every 7 days, so only this remainder (the 'odd days') matters. If the target date lies before the known date, the day shifts backward by the odd-days count; if it lies after, the day shifts forward.

1. 3rd November, 1987 lies before 4th April, 1988, so count the days from the earlier date up to the later one: the remaining days of November (30 − 3 = 27), all of December (31), January (31), February 1988 — a leap year — (29), March (31), and 4 days of April.

2. Total = 27 + 31 + 31 + 29 + 31 + 4 = 153 days.

3. Odd days = 153 mod 7 = 6, since 153 = 21 × 7 + 6.

4. Because 3rd November falls 153 days before the known Monday of 4th April, its day is Monday shifted backward by 6 days: Sunday (1), Saturday (2), Friday (3), Thursday (4), Wednesday (5), Tuesday (6).

5. So 3rd November, 1987 was a Tuesday.

Cross-check: adding 153 days (21 complete weeks plus 6 odd days) forward to Tuesday shifts it forward by 6 days — Wednesday, Thursday, Friday, Saturday, Sunday, Monday — landing on Monday, which matches the given 4th April. This confirms the result.