Ok, I admit I'm a little late, and everyone's probably completely over the fact that there was Friday the 13th this month(Thats assuming they actually thought it was a semi-big deal in the first place!!). Well, since it occurred in the month of February which has 28 days this year, we're going to have another Friday the 13th in the month of March!
Going back to the problem I posed, my high school teacher had a very simple solution to it. It made me feel pretty stupid trying to figure out some super fancy trick to find a solution to this answer. I ended up answering the question as (0,2) -- Meaning that the lowest number possible in a year is zero Friday the 13ths, and the maximum number was 2. Well, the right answer is actually (1,3) -- which caught me totally surprised!!! What it meant was that every year, we are guaranteed to have at least one Friday the 13th. I always used to think it was such a rare occurrence, but I guess it just seemed like it!
Mr. Baker, my high school math teacher who supervised that contest sitting, starting out by assuming 'What if January 1st started on a Sunday????. This would mean that January 13th would actually fall on a Saturday. Since January has 31 days, February 13th would fall on a Tuesday. Again, on a non-leap year, February has 28 days, and so March 13th would also fall on a Tuesday. Following that through, we get the following:
If January 1st was a Sunday then:
Saturday: January, October
Sunday: May
Monday: August
Tuesday: February, March, November
Wednesday: June
Thursday: September, December
Friday: April, July
The above table tells us which days the 13th of that month falls on, assuming that January 1st was a Sunday. So, that year, April 13th and July 13th would fall on a Friday. However, January 1st could have occurred on any one of the 7 days, and we see that no matter which day it fell on, we will always have at least one Friday the 13th occurring each year, and at most, we'll have 3 Friday the 13ths occuring (that is when Feb/Mar/Nov 13 fall on a Friday) -- which will actually happen this year in fact!! We already had Feb 13th fall on a Friday. March 13 will follow soon, and so will Nov. 13th!!
So here you go -- I thought this answer was pretty simple -- The trick I guess is to approach every problem properly, and you can turn a hard problem into a fairly easy one!!!
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