What is the probability that Christmas (on a randomly chosen year) falls on a Monday, Tuesday, Wednesday, &c.? Accounting for the leap years and the 400-year repeating cycle, I wrote a program to model this situation and my answers were:
Sunday 58/400
Monday 56/400
Tuesday 58/400
Wednesday 57/400
Thursday 57/400
Friday 58/400
Saturday 56/400
I verified my answers with my teacher, and they're correct, but I need to solve the problem on pen and paper, without empirically going through every case in a 400-year period. What would be a simple/subtle answer to this? Also, I need to prove most of the assumptions I make in my solution (such as the Gregorian calendar repeating every 400 years).
I found a solution online, and two Stack threads, but I can't really make much sense of it: https://people.missouristate.edu/lesreid/Sol04_0809.html
Thank you :D
