# What is a Fair Word?

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
PRONUNCIATION SPELLING
YETI BIGFOOT
DEEP HIGH
ICY SOLID
DUPLICATE CLOSURE
EVERY SINGLE

CSV version:

Fair Words,Unfair Words
PRONUNCIATION,SPELLING
YETI,BIGFOOT
DEEP,HIGH
ICY,SOLID
DUPLICATE,CLOSURE
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.

• Inspired by this previous question (one of the ideas I had to solve that one, which didn't work, became this one). – Rand al'Thor Dec 23 '20 at 9:29
• is the missing ™ intended? – melfnt Dec 23 '20 at 9:34
• @melfnt Yes - I don't like the idea of "trademarking" puzzles. – Rand al'Thor Dec 23 '20 at 9:46
• Is it relevant whether duplicate is regarded as a verb or a noun? Or is the outcome the same either way? – feelinferrety Dec 24 '20 at 2:20
• Argh almost got one, are you sure bedspread is not a mistake? – Smartest1here Dec 24 '20 at 3:40

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.

• 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). – Rand al'Thor Dec 28 '20 at 19:37
• OK, then I have another proposal, edited into the answer. – Gareth McCaughan Dec 28 '20 at 19:52
• Yep, that's the one I meant. – Rand al'Thor Dec 28 '20 at 19:53