Millennium leap
How many leap years will there be between 2001 and 3001?
Age
11 to 14
Challenge level
Problem
Leap years normally occur every four years. However, years at the turn of a century are leap years only if they are multiples of 400.
Therefore, 2000 was a leap year but the year 1900 was not.
How many leap years will there be between 2001 and 3001?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: There will be 242 leap years between 2001 and 3001.
2001 to 3001 multiples of 4
In 1000 there are 250 multiples of 4
Remove multiples of 100 which are not multiples of 400
2001 to 3001 multiples of 400
2400, 2800 - so out of 10 multiples of 100, only 2 are multiples of 400
250 $-$ 8 = 242