# How to find any day using given date and year?

I am posting after a long time here. I am having trouble finding solution to this types of problem. Please help me out on this case:

If the 1st December, 1994, was Thursday, then what was the day on the same date in year 1995?

All I know it's related to Doomsday rule from Dr. John Conwa, but I need a clear explanation on how the calculation actually works.

• $1995$ was not a leap day so $365 \equiv 1 \pmod 7$. So it should a Friday. – Mohammad Zuhair Khan Apr 22 at 15:52
• The question in the title differs from the one in the body. If you're curious here's about the title one: math.stackexchange.com/q/16945/515527 – Zacky Apr 22 at 16:04

$$1994$$ and $$1995$$ aren't leap years, thus both of them have $$365$$ days.

The same day repeats exactly after $$7$$ days (that's what week is) so basically after $$700$$ days ($$700=7\cdot 100$$) it's still a Thursday.

Now we are $$365$$ days away and $$364$$ is the last multiple of $$7$$ up to $$365$$ thus after $$364$$ days it's still Thursday and obviously after a day it would be Friday.

If it were to be let's say $$20$$ February $$2000$$ a Monday (in a leap year), by the same logic $$20$$ February $$2001$$ would be Wednesday.

• Thank you very much. The rule is cleared to me now. – Md. Imran Hossain Apr 23 at 4:55

Hint:

Taking Dec 1, 1994 (Thursday) as Day-1. What is the date on Day-365 and hence the date on Day-366? What is the day on Day-8? On Day-15? On Day-22?

Can you take it from here?