my name is alan and i'm a year 12 math sc student.

i have this problem which concerns using congruence to find the day of the week of any given date. The question is:

which of your birthdays until your one hundredth, fall on the same day of the week as the day you were born?

i know the general formula for finding out the day of the week. My birthday is on 27th January 1989 so my 100 years will span over two centuries, which will be quite a problem since the formula will only help when dealing with two different years of the SAME century. the fact my birthday is on January (11th month of the previous year) doesn't help either.



Try a simpler approach. All you have to know is that

  1. a common year consists of 365 days, which is 52 weeks plus one day;

  2. a leap year has an extra day in February (so it lasts 52 weeks plus 2 days; and

  3. leap years occur every four years (1992, 1996, 2000, ... ) -- except for some century years, which is not relevant to your problem.

Now make a table. You compute (or look up) that you were born on FRIDAY, (27 Jan, 1989).

year birthday

1989 Fri
1990 Sat
1991 Sun
1992 Mon (Just add one day because the extra day in February followed your birthday.)
1993 Wed (Add two days because there were 366 days between your first and second birthdays.)
1994 ...

You will soon see a 4-year pattern. Note especially the pattern every 28 years! Once you figure out the pattern, you can answer your '100-year' question easily in your head!