# Fred, Fran, and baby makes three

Two mathematicians Fred and Fran were having a baby girl, their first child! They sought the perfect name, a name that would simultaneously reflect togetherness, relationships, and individuality in their burgeoning family. Day and night they debated, rejecting name after name. Finally, they had it! The perfect name!

They named her Erin.

Why?

[Yootleoffer: 1 Yootle for first correct response.]

• 2008/06/18 Addendum: Fred and Fran both study set theory.
• 2008/07/27 Addendum: It turns out I didn’t need the 6/18 hint-addendum: commenters had already chimed in with correct answers but, due to a combination of mechanical and pilot error, I didn’t realize it.

the winner is… John! His is the first correct response. Commenter d is also correct with a more succinct and mathematical explanation. Dennis is close but not quite complete. So I’ll award John 2 yootles, d 1 yootle, and Dennis 1/2 yootle. John and d please let me know your contact info to claim your bounty.

Dennis asks what a yootle is worth. A yootle is a quantified “thanks, I owe you one”. So it’s worth a return favor from me, someone who trusts me, someone who trust someone who trust me, etc.

Bonus challenge: come up with a family of four with the same property and reasonable names (necessarily of eight letters each).

• 2008/08/13 Addendum: The bonus round winner is… aj! He hacked up a script and discovered one of apparently many possible “perfectly” named families of four. Details are in the comments of this post. Thanks aj!

## 14 thoughts on “Fred, Fran, and baby makes three”

1. so each name has exactly two
letters in common with each other:

FRed – FRan
fRaN – eRiN
ERin – fREd

all the names have the same number of letters(4)!
This suggests a natural sense of ‘clustering’ of the names.

3. Okay, the second letter “r” in Erin is there to represent the “togetherness” of their family, since both Fred and Fran have a second letter of r.

The “E” represents Fr”e”ds individuality, while the “N” represents Fra”n”s individuality.

Finally, the “i” comes in because it is the next vowel in the alphabet after “a” and “e”, which are in the third position of Fran and Fred.

Additionally, the “E” could also represent that the mathematicians are putting the family ahead of any individual parts, since e is the letter before F in the alphabet, and both of their names start with F.

I’m confused at to what exactly a Yootle is, but all I seek is gratification if I am right. Fun riddle.

4. John says:

There are three names with four letters.

For any one of the names, all of the following are true:

1. There is one letter that does not appear in either of the other names.

2. There is one letter that appears in both.

3. There is one letter that appears in one of the other two names.

4. The last letter appears in the other of the the other two names.

How do you formalize this?
Also, if they have another daughter, should they name her Ida?

5. Dennis DeCoste says:

Umm … one letter from “Fred” only (E), one letter from “Fran” only (n), one letter from both (r), and one letter from neither (i) –> “Erin”.
Relations, togetherness, individuality.

So … what can my new Yootle buy me these days? … 🙂

6. This is driving me insane. Is there a hint?

7. FoolsGold says:

8. d says:

Every nonempty subset of family members has a unique letter associated with it:

Erin, Fran, Fred: r
Erin, Fran: n
Erin, Fred: e
Erin: i
Fran, Fred: f
Fran: a
Fred: d

9. Thanks everyone! I updated the post with the winner(s).

10. aj says:

Sterling and Sharolyn, meet, marry and multiply, producing twins Courtney and Cordelia:

Generated by:
(a) getting a list of baby names
(b) limiting it to eight letter names, with no duplicate letters
(c) going through every combination of four names, checking that, every pair of names has exactly four letters in common, every triple of names has exactly two letters in common, and all the names together have exactly one letter in common.

I think that’s a sufficient test, but I haven’t proved it — checking after the fact is easy enough.

I think you could do the above a bit more efficiently using a dynamic programming approach (what are the pairs of names with exactly 4 letters in common? from those, what triples have 2 letters in common?, …), but with only 83 eight letter names to start with and a 2GHz laptop it didn’t seem worth the hassle.

There’s actually quite a lot of combinations that work, — limiting it to just boy/boy/girl/girl names from some American census list, I got over a hundred combinations. But a lot involved weird spellings like “krystina” which might or might not count as “reasonable” whatever the census says…

Entertaining anyway 🙂

11. Wow! Fantastic aj. I posed the bonus challenge almost as a joke. My intuition — clearly wrong — was this would be a nearly impossible task. I’d say these names are perfectly reasonable, with nice touches like two of each gender and the same letter (“r”) for the set of all as before. Just to assure myself that it works, I indexed the names by letters in the style of commenter d:

r –> Sterling, Sharolyn, Courtney, Cordelia
n –> Sterling, Sharolyn, Courtney
l –> Sterling, Sharolyn, Cordelia
e –> Sterling, Courtney, Cordelia
o –> Sharolyn, Courtney, Cordelia
s –> Sterling, Sharolyn
t –> Sterling, Courtney
i –> Sterling, Cordelia
y –> Sharolyn, Courtney
a –> Sharolyn, Cordelia
c –> Courtney, Cordelia
g –> Sterling
h –> Sharolyn
u –> Courtney
d –> Cordelia

Thanks for diving into this! Very fun. For what it’s worth I’ll award aj five yootles for this feat.

Dare I suggest next a family of five? OK, you can use first & middle names.

12. aj says:

Hrm, a family of five would need 31 different letters, no? Which, coincidentally would be five more than is in the alphabet — so maybe doable if it was a unique letter for every grouping of the family (with no letter left over, and no letter unique to any individual)…

13. You’re right, aj, good point. One work around would be to treat capital letters differently than lower case letters. Or you could use a slightly larger alphabet that includes some of the common letters with diacritics like Ã©, Ã±, È, etc., or perhaps even allow hyphens, apostrophes, or other somewhat common symbols to count.