Quickly Finding the Day of the Week
Date: 11/14/2000 at 12:37:16 From: V Anand Subject: Day vs date Dear Dr. Math, I have a simple question. Today is November 14, 2000, a Tuesday. What day of the week was November 14, 1901? I got this question in a competitive exam where they expect an answer in 30 seconds. I have seen your calendar chart in the archives, but is there a quick method? Thanks, Anand
Date: 11/14/2000 at 13:03:15 From: Doctor Rick Subject: Re: Day vs date Hi, Anand. Here's what I would do if I only had 30 seconds (and I don't know that I'd make it): That's a difference of 99 years. How many leap years in that time? 99/4 = 24. Add the 24 leap years to the 99 years to get 123. Divide 123 by 7 and get 17, remainder 4. Go back 4 days from Tuesday, and I get Friday. The day of the week for a particular date advances by 1 day every non-leap year, and 2 days every leap year. That's why I added the number of leap years to the number of years elapsed. Then, when the day advances by 7 days, it's back where it started; so I took the remainder on division by 7. Finally, I worked backward to what day it would have to be in order to advance by 4 days and get to Tuesday. I wouldn't have time to stop and think about whether I had properly counted the leap day in 2000, so I wouldn't be quite sure (without further thought) that I had it right. As it turns out, I haven't: I could have seen this by partially listing the leap years between 1901 and 2000: 1904, 1908, ..., 2000. The numbers 4, 8, ..., 100 are 4 times the numbers 1 to 25, so there were 25 leap years. I have to go back one more day, to Thursday. I think this is correct. I've missed the 30 seconds, but we've both learned something. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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