In the gregorian calendar, every year which is divisible by $4$ is a leap year, except for years which are divisible by $100$; those years are only leap years if they're divisible by $400$. (this may seem complicated, but the calendar is carefully designed to keep the average number of days per year very close to the number of days in one complete orbit of the earth.) assuming we keep using the gregorian calendar, how many leap years will there be between $2001$ and $2999$?

242 leap years. 
to find the amount of total possible leap years subtract to find the range 2999-2001 = 998 years. Divide 998 by 4 to get the number of values inside the range divisible by 4.  998/4= 249.5 or 249 total numbers divisible by 4. out of that range only 2100,2200,2900 are divisible by 100 ( 9 possibilities ruled out) but 2400 and 2800 are divisible by 400 and would be a leap year (2 possibilities given back and (7 total exclusions)
249-7 = 242 leap years in that range.