Day of the Week

The history teacher Aarati was explaining about the Indian Independence movement and at last she told that we got independence on Aug 15, 1947. Mahesh’s friend asked the beautiful madam the day of the week on the date. Mahesh knew the answer. He wanted to show off his talent as he had a huge crush on this ma’am. So he made a plan. The ma’am told that she does not know the answer. Then he came to the stage and derived the formula to find the day of the week on any date on the black board. The ma’am was very happy. Ramya knew all this. Mahesh was brilliant but Ramya was more brilliant than Mahesh. Ramya asked whether we can find the day of the week on any date using the formula. Mahesh said yes. Ramya gave two examples. Jan 1, 1 and Sep 7, 1752. Mahesh answered both wrong.

Mahesh had found out a general formula to find the day of the week on a given date. What was that? Why could not he correctly answer Ramya’s questions? Can you find the generalized formula which works on all dates starting from Jan 1, 1?