Math CentralQuandaries & Queries


Question from Madi, a student:

Hi guys,
I have a question. July 4, 1903, was a Tuesday. On what day of the week was July 4, 1904? If you could give me an equation that would work for any question like this, that would be GREAT!
Your fellow math scholar (in training),

Hi Madi,

I won't give you an equation or a formula but I'll show you how to reason out the solution.

First of all July 4, 2003 was on a Friday.

Step 1:

There are $365$ days in a year and $\frac{365}{7} = 52$ with a remainder of $1.$ Thus there are $52$ weeks in a year but the remainder of $1$ means that the calendar gets shifted $1$ day. Thus it looks like July 4, 2004 was a Saturday.

Step 2:

Did your time span include February of a leap year? 2004 was a leap year so yes, your time span did include February of a leap year. Thus at the end of February, 2004 the calendar got shifted one more day and July 4, 2004 was a Sunday.

I hope this helps,

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