If 19 December 1965 was a Sunday, then what day of the week was 20 August 1981?
Thursday
Count the odd days (days left over after full weeks) between the two dates. An ordinary year has 1 odd day and a leap year 2.
Step 1 — From 19 December 1965 to 19 December 1980 there are 15 years, of which 1968, 1972, 1976 and 1980 are leap years: odd days = \(15 + 4 = 19\) \(\equiv 5 \pmod 7\). So 19 December 1980 was a Friday.
Step 2 — From 19 December 1980 to 20 August 1981: 12 (rest of December) + 31 + 28 + 31 + 30 + 31 + 30 + 31 + 20 = 244 days, and \(244 = 7 \times 34 + 6\), giving 6 odd days.
Step 3 — Friday + 6 days = Thursday.
Check: total days = 5723 and \(5723 \equiv 4 \pmod 7\), and Sunday + 4 = Thursday. Friday, Monday and Wednesday would need 5, 1 and 3 odd days respectively.
Thursday option is correct.
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