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On which day of the week did India gain independence in 1947?
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Solution: Step 1: Calculate the number of odd days from 1600 to 1947.
Step 2: 1600 years have 0 odd days, 300 years have 1 odd day.
Step 3: 46 years (from 1901 to 1946) have 11 leap years and 35 ordinary years, which gives 1 odd day.
Step 4: Calculate odd days from January 1, 1947, to August 15, 1947.
Step 5: January to July has 31+28+31+30+31+30+31 = 212 days, and August 15 has 15 days, totaling 227 days = 32 weeks and 3 odd days.
Step 6: Total odd days = 0 + 1 + 1 + 3 = 5.
Step 7: Counting five days from Monday gives Friday.
Step 8: Therefore, August 15, 1947, was a Friday.