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This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.


If a word conforms to a special rule, I call it a Valid Word™.
Use the following examples below to find the rule.

Valid Words™ Not Valid Words™
SAFETY DANGER
OFFICER WORKER
TRAINING TRAIN
SAUCEPAN FRYPAN
ABANDONED RENOUNCED
EXCELLENCE PERFECTION
ASSORTMENT VARIETY
MEANINGFUL MEANINGLESS
COUNTERPOINT BREAKPOINT
AZIDODEDIAZONIATIONS HYDRODEDIAZONIATIONS

And, if you want to analyze, here is a CSV version:

Valid Words™,Not Valid Words™
SAFETY,DANGER
OFFICER,WORKER 
TRAINING,TRAIN 
SAUCEPAN,FRYPAN 
ABANDONED,RENOUNCED 
EXCELLENCE,PERFECTION 
ASSORTMENT,VARIETY 
MEANINGFUL,MEANINGLESS 
COUNTERPOINT,BREAKPOINT 
AZIDODEDIAZONIATIONS,HYDRODEDIAZONIATIONS 

Hint 1:

enter image description here

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2 Answers 2

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A Valid Word satisfies the rule

If we convert each letter to a number ($A=1, B=2,\ldots, Z=26$) and add the values of all but the last letter then the result is congruent to the value of the last letter, modulo $26$. This is like a checksum for the word, similar to the Luhn algorithm used for credit cards as mentioned by FlanMan.

Examples

$S+A+F+E+T = 19+1+6+5+20 = 51 \equiv 25 ($mod $26)$ and $Y=25$

$A+Z+I+D+O+D+E+D+I+A+Z+O+N+I+A+T+I+O+N = 1+26+9+4+15+4+5+4+9+1+26+15+14+9+1+20+9+15+14 = 201 \equiv 19(\mod 26)$ and $S=19$.

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    $\begingroup$ This answer is also valid too :D $\endgroup$
    – Conifers
    Aug 29, 2019 at 9:24
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I tried the following, which failed, but it might give ideas for others to solve this.

After seeing Hint 1, I think the answer is:

A Valid Word™ must somehow pass a credit card-style numerical validation using the Luhn algorithm: https://simplycalc.com/luhn-calculate.php. I converted some Valid Words™ into A1Z26 and to ASCII, but I could not find a way to get them all to pass the Luhn algorithm.

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