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Here are three ways of splitting the letters of the English alphabet into two groups:

1) ABDOPQR; CEFGHIJKLMNSTUVWXYZ

2) BCDGJOPQRSU; AEFHIKLMNTVWXYZ

3) DFHIJLNOPRTUVXYZ; ABCEGKMQSW

In each case, the first collection of letters can be described simply using a one-word 'catchphrase' while the second collection is simply all those letters not in the first collection. First you need to find all the three catchphrases (this should be the only challenging part). In each case, determine how many distinct letters of the catchphrase are in the first and how many in the second collection of letters. You'll then have three pairs of numbers, and your final task is to find which of these three pairs is the odd one out.

What I really hope to achieve in this question is to get a collection of interesting alphabet-splitting puzzles, so that they're not all spread around the site in many different questions. The bit about catchphrases is just to unify this into a single puzzle so that I don't get people telling me I should split this into 3 distinct questions. After this has been solved (which shouldn't take long), I'll throw open the question to editing and we can incorporate all the interesting ways of splitting the alphabet that anyone can think of, and perhaps change or remove the catchphrase and odd-one-out parts of the question. When editing a sequence into the question, please edit the answer into warspyking's now-accepted answer.


Your Puzzles;

4) ABCDEGJLMOQTUZ; FHIKNPRSVWXY

5) EITSANHURDMWG; VLFBKOPJXCZYQ

6) ABCIJOPQRSTUWY; DEFGHKLMNOVZ

7) COPSUVWXZ; ABDEFGHIJKLMNQRTY

8) AHIMOTUVWXY; BCDEFGJKLNPQRSZ

9) ΑΒΕΗΙΚΜΝΟΡΤΧΥΖ; CDFGJLQRSUVW

10) AEFHILMNORSX; BCDGJKPQTUVWYZ

11) HJKMNUVWXY; ABCDEFGILOPQRSTZ

12) BDEFHIKLMNPRTUVWXYZ; ACGJOQS

13) EFPTY; ABCDGHIJKLMNOQRSUVWXZ

14) BCFHIKNOPSUVWY; ADEGJLMQRTXZ


If you think this is a silly way of posing a question, please tell me and give me a chance to improve it before hitting the downvote button. Let's be proactive here! :-)

Edit: I just discovered that more or less exactly the same idea appears in Schott's Miscellany. His list is entitled 'Letter Traits' and is on page 76.

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    $\begingroup$ I like the idea of collecting a bunch of alphabet splitting puzzles in a single post. It might make the most sense to have a question along the lines of "What are some alphabet splitting puzzles?", and have each splitting be a different answer. $\endgroup$ – Julian Rosen Dec 27 '14 at 0:29
  • $\begingroup$ @JulianRosen - Good idea, but probably too late now. You could post this on meta as an idea for a new type of question. Meanwhile, now that squeamish ossifrage has solved this puzzle of mine, let's get to editing! $\endgroup$ – Rand al'Thor Dec 27 '14 at 1:19
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    $\begingroup$ One problem with this idea is how would you downvote one bad puzzle when it's grouped with a bunch of other puzzles? $\endgroup$ – pacoverflow Dec 27 '14 at 6:30
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    $\begingroup$ @warspyking Yes, this is what I meant. But now I'm beginning to think Julian Rosen's idea is better: create a question which just calls for examples of alphabet-splitting puzzles, and then answers will include both the puzzle and (spoilertagged) the solution. There'd be no accepted answer, and the most popular puzzles would rise to the top as Josh Caswell says. Could we have some words from a mod on whether this would be an 'allowed' question format? $\endgroup$ – Rand al'Thor Dec 27 '14 at 12:36
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    $\begingroup$ Meta discussion now open. $\endgroup$ – Rand al'Thor Dec 27 '14 at 12:51
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Final Answer!

Sequences;

  1. ABDOPQR; CEFGHIJKLMNSTUVWXYZ
  2. BCDGJOPQRSU; AEFHIKLMNTVWXYZ
  3. DFHIJLNOPRTUVXYZ; ABCEGKMQSW

ANSWERS (credit to squeamish ossifrage for the 3rd answer):

1) All these letters have enclosed space within the letters; Catchphrase holes.

2) All these letters have curves in them; Catchphrase curves.

3) All letters that correspond with composite numbers from 1 through 26; Catchphrase composite.

NUMBERS:

{1, 4}, {4, 2}, {4, 4}

FINAL ANSWER:

The odd one out is the 1st pair {1, 4} because the other pairs are {even, even} while this one's first number is odd.


OTHER SEQUENCES:

  1. ABCDEGJLMOQTUZ; FHIKNPRSVWXY
  2. EITSANHURDMWG; VLFBKOPJXCZYQ
  3. ABCIJOPQRSTUWY; DEFGHKLMNOVZ
  4. COPSUVWXZ; ABDEFGHIJKLMNQRTY
  5. AHIMOTUVWXY; BCDEFGJKLNPQRSZ
  6. ΑΒΕΗΙΚΜΝΟΡΤΧΥΖ; CDFGJLQRSUVW
  7. AEFHILMNORSX; BCDGJKPQTUVWYZ
  8. HJKMNUVWXY; ABCDEFGILOPQRSTZ
  9. BDEFHIKLMNPRTUVWXYZ; ACGJOQS
  10. EFPTY; ABCDGHIJKLMNOQRSUVWXZ

OTHER ANSWERS:

4) The first group are those letters in the odd columns of a qwerty keyboard.

5) The letters in (in order) the most frequent letters used, sorted just like the morse code sorts them. The latter obviously being least frequent (also in order)

6) The first group are those letters that when spoken in English sound like (or are) words.

7) The first group are those letters that look the same in lower-case as in capitals.

8) The first group are letters which can be reflected in a vertical axis and don't change.

9) The first group are Greek letters (did you notice it?) that look like Latin letters; the second group are Latin letters that don't look like any Greek letter.

10) The first group are letters which names start with a vowel.

11) The first group all have open tops, i.e. they would catch rainwater.

12) The first group all reach the upper left corner of their bounding box.

13) The first group all have an odd number of points where a stroke ends (one or three) where the second group have an even number (zero, two, or four.)

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  • $\begingroup$ I can't for the life of me figure out 3. Does it have to do with locations in the alphabet or just the letters? $\endgroup$ – warspyking Dec 26 '14 at 23:16
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    $\begingroup$ Ha - that's for me to know and you to find out! :-) Any ideas on one-word catchphrases for 1) and 2)? $\endgroup$ – Rand al'Thor Dec 26 '14 at 23:23
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    $\begingroup$ @rand al'thor Define "catchphrase" and give me a nonrelated example please. $\endgroup$ – warspyking Dec 26 '14 at 23:42
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    $\begingroup$ I meant the odd one out to be {4,4} since they're both the same while $1\neq4\neq2$. The moral is that odd-one-out puzzles are bad since they usually don't have unique solutions. $\endgroup$ – Rand al'Thor Dec 27 '14 at 12:33
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    $\begingroup$ Also, I would say 6 is arguable $\endgroup$ – JNF Jul 5 '15 at 9:27
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It looks like warspyking has cracked the first two (I'd suggest holes and curves as catchphrases for these two groups).

I think the catchphrase for The last group is composite. The alphabet positions of the letters that come after the split ("ABCEGKMQSW") are 1, 2, 3, 5, 7, 11, 13, 17, 19 and 23 — i.e., 1 followed by all the prime numbers below 26. All the other numbers are composite, which means they are the product of two or more prime numbers.

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  • $\begingroup$ Well done! You've basically cracked it; you just need the odd-one-out bit to get a pretty green checkmark, and then we can get to editing any alphabet-splitting puzzles anyone can think of into my question. $\endgroup$ – Rand al'Thor Dec 27 '14 at 1:18

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