How many leap years from 1901 to 2100?

Question

How many leap years are there from 1901 to 2100 inclusive? Do it by counting rather than by listing two hundred years. State the leap-year rule, explain why the naive answer of 50 is wrong, and say how many leap years a full 400-year cycle contains.

Accepted Answer

49. The rule. A year is a leap year if it is divisible by 4, except that years divisible by 100 are not, unless they are also divisible by 400. So 1900 was not a leap year, 2000 was, and 2100 will not be. The count. Years divisible by 4 from 1901 to 2100: the first is 1904 and the last is 2100, giving (2100 minus 1904)/4 + 1 = 49 + 1 = 50 candidates. Among them the century years are 2000 (a leap year, divisible by 400) and 2100 (not a leap year). Remove 2100: 49 leap years. Why 50 is tempting. Two hundred years divided by four is fifty, and people forget the century exception. Over the two ce…

How many leap years from 1901 to 2100?

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