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Corny birthday math

Mark as a kidSix years ago, Mark and I were both prime.

This year, Mark and I once again share prime ages.

And, in another six years, we'll be prime together for the last time until eighteen years hence.

Can you guess how old Mark turned today?

(I actually have no idea if this math problem is possible to solve using only the information presented here. But I'll be curious to see if Roland tries!)



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age
I think I solved it, but I have the advantage of knowing when you graduated college and thus your approximate age.
Comment by rebecca Sun Jan 10 09:12:08 2016
Rebecca --- So what's your guess? I don't mind you outing our ages to the world and presumably anyone else will try to decipher the math before they scroll down. :-)
Comment by anna Sun Jan 10 09:47:16 2016
37
Comment by Anonymous Sun Jan 10 10:14:29 2016
Mark is 47 today right?
Comment by Justin Noce Sun Jan 10 11:20:17 2016
age

Mark's 47... You 37, (18 years = 71 and 61) 6 years ago, 41 and 31... Happy birthday...

Comment by Dan Mott Sun Jan 10 11:51:42 2016
You guys are math whizzes! I'm impressed! :-)
Comment by anna Sun Jan 10 11:59:10 2016
yep I got 37 and 47.
Comment by Rebecca Sun Jan 10 14:18:21 2016
I'm an artist and mostly allergic to math, but happy birthday Mark!
Comment by Deb Sun Jan 10 17:09:23 2016

Hi All,

So much fun to read your column :).

Happy Birthday !!!!!!

John

Comment by John Sun Jan 10 18:03:34 2016

It's close, but I don't think it's enough information without further knowledge. Here's what the data you supplied gives (using ipython because doing it by hand would be too tedious):

In [1]: import numpy as np

In [2]: primes = np.array([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97])

In [3]: set(primes-6) & set(primes+6) & set(primes+18) & set(primes)
Out[3]: {23, 37, 47}

So the correct ages are in there.

If you were to add e.g. that there's 10 years between you, only one answer would remain;

In [4]: set(primes-6) & set(primes+6) & set(primes+18) & set(primes) & set(primes-10)
Out[4]: {37}
Comment by Roland_Smith Sun Jan 10 18:19:16 2016

Deb -- Sorry to inflame your allergy! :-)

Roland --- I love your mathematical analysis! Of course, the human reader would look at the header ("homesteading year 10") and realize that we can delete all numbers less than 28 assuming we began homesteading in adulthood. On the other hand, they might not be able to tell who is older --- me or Mark --- which would still leave two numbers in the possible solution set. So, you're right --- I need to add more data to my word problem next time around!

Comment by anna Sun Jan 10 18:32:51 2016
Happy Birthday! I, too, am allergic to Math. It gives me headaches. LOL
Comment by Emily Mon Jan 11 11:49:24 2016