If 8th April 2012 was a Tuesday, what would be the day on 21st November 2012?

To find the day of the week on a target date given a known day on a start date, count the total number of days between the two dates, divide that count by 7, and the remainder — called the number of ‘odd days’ — tells you how many weekdays forward the target date falls from the known start day. This works because the seven weekdays repeat in a fixed 7-day cycle (arithmetic mod 7).

1. Days left in April after the 8th: 30 - 8 = 22 days.

2. Full months between April and November: May (31) + June (30) + July (31) + August (31) + September (30) + October (31) = 184 days.

3. Days counted in November up to the 21st: 21 days.

4. Total days between the two dates: 22 + 184 + 21 = 227 days.

5. Odd days: 227 ÷ 7 = 32 weeks with a remainder of 3, so there are 3 odd days.

6. Starting from Tuesday and moving forward 3 odd days: Tuesday → Wednesday → Thursday → Friday.

Check: 32 complete weeks account for 32 × 7 = 224 days, and 224 + 3 = 227, matching the total day count above, so the 3 odd-day shift is confirmed.

So 21st November 2012 falls on Friday.