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This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and their spin-off What is a Number™ series.

I like What is an Adjective Noun™ puzzles. Here are a few I prepared earlier:

Let's start off with an easy word puzzle:

Fringe Words™

Fringe Words™, Not Fringe Words™
AMNESIA,CHOPPING
ISRAELI,PARROT
REVOLVER,BEEKEEPERS
CLASSIC,DISAPPOINT
RAZOR,BAAS
AROMA,SUBTERRANEAN
FLAGSTAFF,SLEEVE
TOILET,TWIDDLED

We've had many Phrase™, Word™ and Number™ puzzles. So why not a Set™ puzzle?

NB: Sets are intentionally sorted for your (in?)convenience

Leaping Sets™

Leaping Sets™, Not Leaping Sets™
{5,11,19,27,29,37,65,81},{8,24,32,36,50,54}
{12,21,23,34,76,89,90,98},{10,12,20,27,32,40,64}
{2,8,10,11,16,17,23,47,63},{11,36,45,63,72,100,144}
{2,6,8,11,22,23,25,26,28},{30,40,80,100,190,250,320}
{2,7,18,19,35,48,52,66,90},{15,16,18,27,45,53,62,135}
{12,21,24,27,39,72,78,87,93},{23,35,40,53,70,80,106,160}
{15,25,35,40,75,95,100,120},{36,63,189,234,345,567,981}
{12,18,21,41,61,91,100,162},{3,9,11,17,27,41,63,89}
{21,28,35,91,119,126,140},{24,32,48,75,80,96,120}

Let's go back to words again:

Persistent Phrases™

Persistent Phrases™,Not Persistent Phrases™
BLACK HAT,ADD THE HEAD
NEW STUN GUN,AN ONGOING GAG
THE TINY CAT,AND END ALL THE CHAT
I LIKE TRAINS,TAKE THE HALL
QI SQUARE,BET A TAB
YOUR USUAL SUSPECTS,HE LOOPS THE POOLS
BIG BIKE RIDER  WAY TOO,LITTLE WAY TOO LATE
TOO LITTLE YET TOO LATE,IS NOT TO SIT
YOU'RE YELLING LOUDLY,SHE'S RATING THE TRAINS

Sorry, but I couldn't resist calling them Square Numbers™:

Square Numbers™

Square Numbers™,Not Square Numbers™
9517,2662
8246,46857
10338,819927
291461,791630
240264,30182063
48137271,26649381
91044019,37199173
248163927,7919191917
951926291,89458281746
15949392919,3883929171846

Finally, let's go full circle and return to a Word puzzle.

Double Jump Words™

Double Jump Words™,Not Double Jump Words™
POPULAR,BEDBUG
COLOUR,DOWNPOUR
FAULTLESS,COMMUTE
POLYSYLLABIC,BIPARTISAN
ASYMPTOTE,ASSUMING
PICCOLO,SQUIRE
EXPONENT,OUTVOTE
KARATE,ABDUCTION
BOLDLY,MUSEUM
HUMIDITY,MAHJONG
ROTATION,MANPOWER
FLYBY,AMOEBA

From this selection of puzzles, can you tell me what quality is essential to make an Interesting Puzzle™?

Not all puzzles are without flaws, and good is intrinsically related with bad. Can you also tell me what quality this puzzle might have that isn't necessarily desirable, and makes a puzzle less Interesting™?

Good luck!

Hint level 0 (thanks for the idea, @Rubio) (Leaping Sets™)

All of the tags are there for a reason

Hint level 1 (Leaping Sets™)

Mea Culpa Nay had a good idea

Hint level 0 (Square Numbers™)

Square won't help with the property

Hint level 1 (Square Numbers™)

You need to find both the property and the manner of decryption

Hint level 1.5 (Square Numbers™)

Look at hint 0... how could square be useful then? (Hint hint look at hint 1)

Hint level 2 (Square Numbers™)

So, $\text{numbers}\rightarrow\text{some sort of square}\rightarrow\text{letters}$...

Hint level 3 (Square Numbers™)

In particular, we a looking for a cipher that takes a number, puts it through some sort of square and gets a letter (and vice versa)

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  • 2
    $\begingroup$ I see a zendo metapuzzle coming up... $\endgroup$
    – Wen1now
    Sep 5, 2017 at 0:11
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    $\begingroup$ Everyone is so bad at number sequences though :( $\endgroup$
    – Totumus Maximus
    Sep 6, 2017 at 8:55
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    $\begingroup$ What is there reason for spamming ™ everywhere? $\endgroup$
    – reducing activity
    Sep 6, 2017 at 11:52
  • $\begingroup$ @MateuszKonieczny it means it is all part of the meta-puzzle. $\endgroup$
    – Totumus Maximus
    Sep 6, 2017 at 11:54
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    $\begingroup$ @MateuszKonieczny It also follows the standard for a recurring puzzle type on this site (you should see many "What is a(n) Adjective Noun™" puzzles under "Related" on the sidebar) $\endgroup$
    – feelinferrety
    Sep 6, 2017 at 17:08

6 Answers 6

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Subpuzzles

A Fringe Word™

has the same letters on the ends. Those letters spell AIRCRAFT.

A Not Fringe Word™

has a double letter somewhere in the word. Those letters spell PREPARED.

A Leaping Set™

has three numbers in arithmetic progression. Going a step back from the first number in that progression and indexing into the alphabet gives CAESAREAN.

A Not Leaping Set™

has three numbers in geometric progression ($b=ka, c=kb$). Going back one step, just as for Leaping Sets™, and 1-indexing into the alphabet gives an answer of PERPETUAL.

A Persistent Phrase™

has a letter common to all words. Those letters spell out ANTIQUITY.

A Not Persistent Phrase™

has a letter appearing in only one word. Those letters spell out TICKETING.

A Square Number™

Does not have two adjacent digits that are in the set {6, 7, 8, 9, 0}. They also have two adjacent digits inside the set {1, 2, 3, 4, 5}, using those as indices on Polybius square yields VINDICTIVE.

A Not Square Number™

Has two adjacent digits that are in the set {6, 7, 8, 9, 0}. Using those as indices on a Polybius square yields ACTIVATION.

A Double Jump Word™

has two identical letters with a gap of length 1 in between. Those letters spell out POLYTONALITY.

A Not Double Jump Word™ has

two consecutive letters differing in position in the alphabet by 2. Looking at the letters that would go in between them gives CONSTRUCTION.

So what makes an Interesting Puzzle™?

If we look at the answer words...

all the positive answers:
AIRCRAFT
CAESAREAN
ANTIQUITY
VINDICTIVE
POLYTONALITY

They all have the pattern ...AB...BA... in them somewhere. That is, a single bigram (two-letter pair) in the word once is reversed elsewhere in it. Taking those bigrams and putting them together gives CREATIVITY (which also has the pattern that its subpuzzle answers do!).

And what makes a not-Interesting Puzzle™?

Let's look at all the negative answer words:
PREPARED
PERPETUAL
TICKETING
ACTIVATION
CONSTRUCTION

They all have the pattern ...AB...AB... in them somewhere. That is, a single bigram appears in the word twice. Taking those bigrams and putting them together gives REPETITION (which also has the pattern that its subpuzzle answers do! as a bonus, it's nicely thematically connected to the extraction method!)

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  • $\begingroup$ Good job @Pufe! This puzzle can finally be put to rest. $\endgroup$
    – boboquack
    Oct 6, 2017 at 0:42
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Partial answer:

@thecoder16 has noted what a Fringe Word™ is, and it gives:

AIRCRAFT (taking each outer letter)

A Persistent Phrase™ has:

A letter that occurs in all words within the phrase

Which gives:

ANTIQUITY (taking the common letter from each phrase)

A Double Jump Word™ has:

a repeated pair of letters, separated by another letter

Which gives:

POLYTONALITY (taking the repeated letter from each word)

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  • $\begingroup$ ah, as usual i fail to read between the lines. do you have any idea what these words will do? $\endgroup$
    – Quintec
    Sep 5, 2017 at 0:51
  • $\begingroup$ @thecoder16 Not yet... though I note that the first one is a member of the latter one... $\endgroup$
    – Alconja
    Sep 5, 2017 at 0:53
  • $\begingroup$ would be an interesting idea, but sadly not all the puzzles are word based $\endgroup$
    – Quintec
    Sep 5, 2017 at 0:56
  • $\begingroup$ The "Not" column is another word puzzle, I've found patterns in "Not Fringe" and "Not Persistent" you can check out if you want. Still no luck on "Not Double Jump." The words don't seem to mean anything. Or if they do I'm not seeing it with 5. $\endgroup$
    – Braydon
    Sep 5, 2017 at 1:13
  • $\begingroup$ @Braydon - Yeah, just noticed your answer. Nice find. $\endgroup$
    – Alconja
    Sep 5, 2017 at 1:18
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It appears there is a puzzle to the "Not Fringe Words" as well.

Each "Not Fringe Word" has a double letter in the middle. Taking each double letter spells "PREPARED"

A "Not Persistent Phrase" is one where

Only one letter does not appear multiple times in the phrase. Taking the single letter gives the word "TICKETING"

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Partial

A "Not Double Jump Word" is one which

Contains a single consecutive pair of letters that differs by 2 places in the alphabet. Taking the letter between these two in each word gives "CONSTRUCTION".

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5
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Partial(more added if I find them)

This seems almost TOO obvious, but a Fringe Word™ is

a word that starts and ends with the same letter.

A Double Jump Word™ is

a word that has a letter, a different letter, and then that first letter repeated. Ex. POP, OLO, LTL (the first three Double Jump Words™ in the list)

EDIT: based on everyone's finds, it seems the quality of an Interesting Puzzle is

The not xxx side also has a single defining quality, and you can take the qualities of each side to make words.

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  • $\begingroup$ Though this is true, this isn't the final answer. $\endgroup$
    – boboquack
    Sep 6, 2017 at 0:25
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    $\begingroup$ This is a metapuzzle - all the answer words will be used for something. We just don't know how yet. $\endgroup$
    – Deusovi ♦
    Sep 6, 2017 at 0:38
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Well, partial answer, for leaping sets:

EDIT

At least two pairs of numbers are there in the Leaping Sets (which are obtained by skipping/leaping by at least 4 numbers [and hence perhaps the word leap] for one pair and varying number for the other pair) whose DIFFERENCES are the same, which is the not the case with the Non Leaping sets.

For example:

Consider first leaping set: 5,11,19, 27,29,37, 65,81 in which we can find the two pairs (11,65) and (27,81) as having the same skipping/leaping difference of 54. The same is not seen in its counterpart.

Similarly, for the second set

which is 12,21,23,34,76,89,90,98, we can consider (12,89) and (21,98) as the pairs. Notice that '21', '23', '34', '76' and '23', '34', '76', '89', '90' were leapt over!.

Hope this satisfies the title of the part of this puzzle!

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    $\begingroup$ In the second-last non-leaping set, there are the pairs ${3, 9}$ and ${11, 17}$, which disprove this theory. $\endgroup$
    – GentlePurpleRain
    Sep 7, 2017 at 18:23
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    $\begingroup$ In the second non-leaping set, there are the pairs $12,32$ and $20,40$, each of which leap over other numbers, which disprove this latest theory. $\endgroup$
    – boboquack
    Sep 8, 2017 at 3:59
  • $\begingroup$ Too bad he is the only one who tried to solve this puzzle further :( $\endgroup$
    – Totumus Maximus
    Sep 8, 2017 at 15:50
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    $\begingroup$ @TotumusMaximus: I think several people have tried to solve the numerical puzzles. Mea Culpa is just the only one who posted an answer. (And with meagre success, it seems.) $\endgroup$
    – M Oehm
    Sep 8, 2017 at 16:15
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    $\begingroup$ I don't explain why the downvotes are there, I was the one who upvoted your answer. $\endgroup$
    – 1357924680a
    Apr 12 at 15:44

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