Question

How many times does the 29th day of the month occur in 400 consecutive years?

Answer 1

So it would be February 29

This is called a leap year.

It occurs every four years.

Answer 2

Yeah, I got that. So, Total number of months ( excluding February) + Februaries in leap years?

Answer 3

Wouldn't the number of leap years in 400 years be 100? :?

Answer 4

Every 4 years is a leap year...

So:
\[\frac{ 400 }{ 4}=100 \]
\[100 \times 12=1200\]

Answer 5

Yeah, so shouldn't it be 4500?
But why does the answer say 4497?

Answer 6

So then the leftover is:
\[300 \times 11=3300\]
Therefore:
\[3300+1200= 4500\]

So:
4500 times in 400 years

Answer 7

you don't always have a leap year every 4 years

Answer 8

really? huh didn't know that 0.o

Answer 9

Oh, right. I got it. Like, for example : Year 100, 200 and 300 are not leap years?

Answer 10

correct

Answer 11

Oh right....

damn didn't see that lol

thank you @Zarkon :)

Answer 12

so during a 400 year period you should have 3 days that normally are leapyears but because that are divisible by 100 (and not 400) they are not

Answer 13

When it comes to two 00s in the end, then you will divide it by 400 to check whether it is leap year or not..

Answer 14

Like, in case of 1500, there is two 00s in then end so divide it by 400 here, not divisible so 1500 is not a leap year..

So do 100, 200, 300..

Answer 15

Thank you, I think I get it now. ^^ So, it's 2500 - 3 = 4497.

Answer 16

\[2500 - 3 = 2497\]

lol error :)

Answer 17

Lol, my bad. -.-
I meant 4500 - 3. :P

Answer 18

yup :P