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A Really Weird Math Problem (Posted on 2018-03-12) Difficulty: 2 of 5
On The Big Bang Theory's episode "The Athenaeum Allocation", Sheldon mentions to Amy that for their proposed wedding date, May 12,

"The month squared equals the square of the sum of the members of the set of the prime factors of the day. Isn't that romantic?"

Amy's reply contorts a Shakespeare quote: "shall I compare thee to a day that's also a really weird math problem?"

It's indeed weird as the squaring is introduced for no reason at all.

But also, how rare is the circumstance? What other dates of the year exhibit the property? Remember that because of the set-membership criterion, each prime factor is included in the sum only once: 12 has prime factors 2 and 3, and those add up to 5, for May.

  Submitted by Charlie    
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Solution: (Hide)
Of course there are February 2, March 3, May 5, July 7 and November 11.

February 4, 8 and 16 are almost as trivial, as are March 9 and 27 and May 25.

Then we get to the meat: May 6, 12 (the original), 18 and 24.
July 10 and 20
August 15
September 14 and 28
October 21 and 30

That's 22 dates of the year including May 12.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionThere are N datesDej Mar2018-03-12 17:38:04
re: Spoiler (I think . . .)Charlie2018-03-12 14:10:03
Spoiler (I think . . .)JayDeeKay2018-03-12 11:56:10
Solutionarmando2018-03-12 11:14:39
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