Calendar and Leap Year

Number Theory Level pending

A standard calendar year has $365$ days. A leap year has $366$ days. A year is a leap year if it is divisible by $4$ , except if it is a century year not divisible by $400$ . So the year $1900$ was not a leap year( since $1900$ is not divisible by $400$ , but $2000$ was a leap year since $2000$ is divisible by $400$ ). December $25, 2013$ was a Wednesday. What day of the week will be Dec $25, 3013$ ?

Sunday Monday Thursday Wednesday Friday Saturday Tueday

1 solution

Hana Wehbi
Oct 31, 2016

If we divide $365$ by $7$ , we get a remainder of $1$ . This means that without leap years, the days of the week for a particular calendar date would advance $1$ day per year. There is $1000$ years from $2013$ to $3013$ , so this would account for $1000$ added days . However, we must then add this number to the $250=1000/4$ leap days and subtract the non-leap days in the new century that are not divisible by $400$ , there are $8$ of these, giving a total $1000+250-8=1242$ . Divide $1242$ by $7$ to get a remainder of $3$ . This means Dec $25, 3013$ will occur $3$ days after Wednesday, which is Saturday.

Calendar and Leap Year

1 solution

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