8
$\begingroup$

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.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{3.5}} \def\Title{\textbf{ Valid }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ SAFETY }&\text{ DANGER }\\ \hline \text{ OFFICER }&\text{ WORKER }\\ \hline \text{ TRAINING }&\text{ TRAIN }\\ \hline \text{ SAUCEPAN }&\text{ FRYPAN }\\ \hline \text{ ABANDONED }&\text{ RENOUNCED }\\ \hline \text{ EXCELLENCE }&\text{ PERFECTION }\\ \hline \text{ ASSORTMENT }&\text{ VARIETY }\\ \hline \text{ MEANINGFUL }&\text{ MEANINGLESS }\\ \hline \text{ COUNTERPOINT }&\text{ BREAKPOINT }\\ \hline \text{ AZIDODEDIAZONIATIONS }&\text{ HYDRODEDIAZONIATIONS }\\ \hline \end{array}$$

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

$\endgroup$
4
$\begingroup$

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 $S=19$.

$\endgroup$
  • 1
    $\begingroup$ This answer is also valid too :D $\endgroup$ – Conifers Aug 29 at 9:24
1
$\begingroup$

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.

I only have a cell phone with me at the moment, so it is hard to test many ways of computing the numbers.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.