India celebrated its first Republic Day on 26th January 1950. What day of the week was it?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Thursday
Count the odd days (days left over after whole weeks) from the start of the calendar up to the date; 0 odd days means Sunday, 1 Monday, 2 Tuesday, 3 Wednesday, 4 Thursday, 5 Friday, 6 Saturday. 26th January 1950 comes after 1949 complete years and 26 days.
1600 years: 0 odd days (every 400 years give 0)
Next 300 years (1601 to 1900): 1 odd day
1901 to 1949: 49 years with 12 leap years (1904, 1908, …, 1948) and 37 ordinary years: \(12\times2+37\times1=61\) odd days
\(61=8\times7+5\), so 5 odd days
1 to 26 January 1950: 26 days \(=3\times7+5\), so 5 odd days
Total \(=0+1+5+5=11=7+4\), that is 4 odd days
4 odd days means Thursday