Born on 29 February, how many birthdays by age 40?

Question

A child is born on 29 February 2000. By the time they are forty years old (the day 29 February 2040 rolls around), how many actual 29 February birthdays have they had, counting the 2040 one but not the day they were born? Watch the century rule: not every year divisible by 4 is a leap year.

Accepted Answer

Ten birthdays. The leap years. The candidate years are 2004, 2008, 2012, 2016, 2020, 2024, 2028, 2032, 2036 and 2040. The century rule only removes years divisible by 100 that are not divisible by 400, and none of those (2100 is the next) falls in this range. So all ten are genuine leap years, and each has a 29 February. That is ten true birthdays in forty years. Why 2000 itself was fine. The year 2000 is divisible by 400, so it was a leap year despite being a century year, and 29 February 2000 really existed. Had the child been born on 29 February 1900... they could not have been, because 19…

Born on 29 February, how many birthdays by age 40?

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