How would you solve this day of the week question?

Factual Questions
1

A contestant on Are You Smarter than a 5th Grader lost at the 25,000 level and it stumped most of the kids in the classroom. Even the kid helping the contestant blew the answer and his “save”.

What day of the week must the 1st occur on if the month has a Friday the 13th?

Trial and error, and counting on your fingers will get the answer. The contestant said Tuesday and obviously didn’t double check the count using his fingers. :wink:

M,T,W,Th,F,Sat,S,M,T,W,Th,F,Sat Nope that’s not it. :smack:
back up a day and count it out again. :wink:
S,M,T,W,Th,F,Sat,S,M,T,W,Th,F

“Jeff, Sunday is the answer”

Easy enough without cameras, a noisy crowd, a snarky host, and a time limit.

Is there a mathematical expression to solve this?

Trial and error with brute force seems a bit unsatisfying.

2

I’d go forward to subtract a full week: if Friday is 13, then Sat. is 14, and Sun 15 - subtract 2 weeks, Sun = 1.

But IAMNAMathematician.

3

The same day is always seven days apart. If the 13th is a Friday then the other Fridays in the month are the 6th, 20th, and 27th. You want the 6th and then go five days earlier. That’s Sunday. Or you can go forward as constanze did.

Mathematically, this is an example of using modular arithmetic in mod 7.

4

I’d normally use Exapno Mapcase’s method; except in this case I just know off the top of my head that a month that starts on Sunday will have a Friday the 14th. If the question had been about Tuesday the 22nd I’d have to do some figuring.

ETA: 22-21=1 so the first day would also be Tuesday :slight_smile:

5

Thanks. I knew there had to be an area of math that covered this.

6

The trick is of course you think, “the 14th is a Saturday, so 2 eeks before that must be a Saturday.” But 2 weeks before the 14th is the 31st (or 30th, or 28th) of the month before. Requires a bit more of a stop-and-think. Sometimes the trick to a trick question isn’t a trick.

7

Going on 22 years of working in libraries has accustomed me to keep track of dates in my head a little, and the easiest way (for me) that I’ve found to do it is to keep track of which day of the week the 7s fall on. Knowing that a Friday is the 13th means Saturday is the 14th means that the first was a Sunday for reasons mentioned above. It’s mostly habit for me now.

This month the 7s fall on Wednesdays, FWIW.

8

See, it seems easy in our heads, when we’re watching, but put us under the glare of the studio lights in front of everyone, or maybe just a computer screen in privacy of our own home, and it’s easy to mess up somewhere.

[I assume the poster meant to write “13th” there?]

9

Without reading any more than just this, I would say that like the 7th, 14th and 21st all share the same day of the week, that the 1st of the month must have the same day as the 15th. Therefore if the 13th is a Friday, then the 15th (and likewise, the 1st) must be a Sunday.

10

I can’t imagine having Jeff Foxworthy yammering away at you is good for anyone’s thought process. Not that the contestants on AYSTAFG? were rejected by Jeopardy for being too knowledgeable.

11

:smack: I did.

12

It’s obviously two days after Friday the -1st.

13

If the 13th falls on a Friday, then two days later the 15th falls on a Sunday. So that means that the 1st (i.e. a fortnight earlier), must also fall on a Sunday.

14

I don’t get how even the kids couldn’t get this, even if all they did was count backwards. If the thirteenth is a Friday, then the twelfth is a Thursday, then the eleventh is a Wednesday, etc. You just use your fingers. I definitely don’t see what line of reasoning would lead not one but two people to conclude that it was on a Tuesday.

15

The fingers method was pretty easy. Hold up seven fingers (one for each day of the week), start on the sixth finger (friday) as 13 and count backwards from there and see what finger you land on when you get to the first.

16

My quick thoughts would have been “Thirteen days is about two weeks. If Saturday had been the first, then it would be Friday the fourteenth. So the first must be a Sunday.”

17

I actually thought it through as “Saturday is the 14th. So Saturday would be the 0th. So Sunday is the first.” I find it easier if I don’t arbitrarily start the month on the 1st. :slight_smile:

I guess I’m not the only one. :slight_smile:
-D/a

18

I am a mathematician, and this is the way I solved it.

19

Am I the only person who could simply instantly say “Sunday”? It’s not like none of us have ever seen a calendar before.

20

I’m with Scarlett87. Unbelievable. For me this wouldn’t even have required math (I try to avoid things that require math).