Question 136

How many times does the 29th day of the month occur in 400 consecutive years?

Solution

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In every year, 29th date appears 11 times i.e. in every month except February.
This will amount to 11*400 = 4400 times.
However, in every leap year, 29th date appears 1 more time in February.
So, the number of leap years:
Years divisible by 4: 400 / 4 = 100
Subtract non-leap century years (divisible by 100 but not 400): -3 (e.g., 100, 200, 300)
Total leap years = 100 - 3 = 97 occurrences.
So, total occurrences = 4400 + 97 = 4497.

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