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If a word conforms to a special rule, I call it a Fair Word. If it does not conform to this rule, I call it an Unfair Word. Here is a list (not exhaustive) of some Fair Words and Unfair Words:

Fair Words Unfair Words
BEDSPREAD DUVET
PRONUNCIATION SPELLING
YETI BIGFOOT
DEEP HIGH
ICY SOLID
DUPLICATE CLOSURE
BADLY WELL
EVERY SINGLE

CSV version:

Fair Words,Unfair Words
BEDSPREAD,DUVET        
PRONUNCIATION,SPELLING   
YETI,BIGFOOT      
DEEP,HIGH         
ICY,SOLID        
DUPLICATE,CLOSURE      
BADLY,WELL    
EVERY,SINGLE

Main question: find the rule which determines Fair Words and Unfair Words.

Bonus question: which of the above Fair Words is a Super-Fair Word?

Hints and further information:

  • The order of the words doesn't matter.

  • There is no significance in the particular choice of Unfair Words: they're just words vaguely similar to the Fair Words opposite them which are not Fair.

  • The meaning of the words doesn't matter.

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  • $\begingroup$ Inspired by this previous question (one of the ideas I had to solve that one, which didn't work, became this one). $\endgroup$ Commented Dec 23, 2020 at 9:29
  • $\begingroup$ is the missing ™ intended? $\endgroup$
    – melfnt
    Commented Dec 23, 2020 at 9:34
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    $\begingroup$ @melfnt Yes - I don't like the idea of "trademarking" puzzles. $\endgroup$ Commented Dec 23, 2020 at 9:46
  • $\begingroup$ Is it relevant whether duplicate is regarded as a verb or a noun? Or is the outcome the same either way? $\endgroup$ Commented Dec 24, 2020 at 2:20
  • $\begingroup$ Argh almost got one, are you sure bedspread is not a mistake? $\endgroup$ Commented Dec 24, 2020 at 3:40

1 Answer 1

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A word is Fair if

when you convert the letters to numbers by A1Z26, it contains both some number and its square. BEDSPREAD, PRONUNCIATION, YETI, DEEP, ICY, DUPLICATE (this one is Super-Fair because it happens twice), BADLY (this one is kinda Super-Fair if you count A/A...), EVERY.

The name

presumably comes from the idiom "fair and square".

OP indicates in comments that I guessed wrong about what counts as Super-Fair. Here's another possibility that works about as well:

BEDSPREAD is Super-Fair because it has B^2=D and then D^2=P.

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  • $\begingroup$ Congrats, you got it. Although you're not quite right on the bonus question (hint: I didn't consider happening twice unconnectedly to be a Super occurrence). $\endgroup$ Commented Dec 28, 2020 at 19:37
  • $\begingroup$ OK, then I have another proposal, edited into the answer. $\endgroup$
    – Gareth McCaughan
    Commented Dec 28, 2020 at 19:52
  • $\begingroup$ Yep, that's the one I meant. $\endgroup$ Commented Dec 28, 2020 at 19:53

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