# What is a Valid Word™?

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:

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 $$S=19$$.

• This answer is also valid too :D Aug 29, 2019 at 9:24

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.