How many times in 1900 did the 1st day of the month fall on a Tuesday?
Hint: The year 1900 was not a leap year.
The number of days in a month modulo 7 can be used to very quickly compute the day at the start of the next month if you know the starting day of the previous month. For example, if April 1st was a Wednesday, then May 1st will be a Friday since April has 2 modulo 7 days (Wednesday+2 days, if you like!)
In order to answer ...
This provides an example of using congruence to find days and dates.