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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?

 Apr 14, 2019
 #1
avatar+102921 
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2999 - 2001  =  998 years

 

Number of possible leap years  =  floor (998 / 4)  = 249 years

 

But    2100    2200   2300  2500  2600  2700  2900 will not be evenly divisible by 400

 

So

 

249 - 7  =   242 leap years

 

cool cool cool

 Apr 14, 2019
 #2
avatar+178 
+1

Thanks CPhill! I got 243 and did 249-6 instead of 249-7! Now I understood my really silly mistake :)

 Apr 14, 2019
 #3
avatar+102921 
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I think I got the same answer when I did it before....I believe I omitted one of the leap years....!!!

 

 

cool cool cool

CPhill  Apr 14, 2019
 #4
avatar+178 
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Yeah I think I did the same the first time I solved it

Rudram592  Apr 14, 2019

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