# What is a Commutative 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 Commutative Word™.
Use the following examples below to find the rule.

$$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{1}} \def\Title{\textbf{ Commutative }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ DAD }&\text{ MOM }\\ \hline \text{ BIND }&\text{ TIE }\\ \hline \text{ AXES }&\text{ HOES }\\ \hline \text{ COVER }&\text{ REVEAL }\\ \hline \text{ CHINA }&\text{ KOREA }\\ \hline \text{ FLIRTY }&\text{ CUTESY }\\ \hline \text{ BOILED }&\text{ FRIED }\\ \hline \text{ DOUGLAS }&\text{ MATTHEW }\\ \hline \text{ SESSIONS }&\text{ COOKIES }\\ \hline \text{ LEGALIZE }&\text{ JUSTIFY }\\ \hline \end{array}$$

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

Commutative Words™,Not Commutative Words™
BIND,TIE
AXES,HOES
COVER,REVEAL
CHINA,KOREA
FLIRTY,CUTESY
BOILED,FRIED
DOUGLAS,MATTHEW
LEGALIZE,JUSTIFY

• rot13(V nz gelvat gb svther bhg ubj guvf zvtug or eryngrq gb gur pbzzhgngvir cebcregl ol erneenatvat gur yrggre gb znxr qvssrerag jbeqf, fb sne ab yhpx. Nz V ng yrnfg ba gur evtug genpx?) – GrumpyLlama59 Sep 23 at 22:22
• Whenever I see Commutator, I think: Rubik's Cube... – P1storius Sep 24 at 13:40

A commutative word is a word in which

When converted A1Z26, the multiplication of the first two numbers equals the sum of the rest

Proof:

DAD -> 4 1 4 -> 4*1 = 4

BIND -> 2 9 14 4 -> 2*9 = 14+4 (=18)

AXES -> 1 24 5 19 -> 1*24 = 5+19 (=24)

COVER -> 3 15 22 5 18 -> 3*15 = 22+5+18 (=45)

CHINA -> 3 8 9 14 1 -> 3*8 = 9+14+1 (=24)

FLIRTY -> 6 12 9 18 20 25 -> 6*12 = 9+8+20+25 (=72)

BOILED -> 2 15 9 12 5 4 -> 2*15 = 9+12+5+4 (=30)

DOUGLAS -> 4 15 21 7 12 1 19 -> 4*15 = 21+7+12+1+19 (=60)

SESSIONS -> 19 5 19 19 9 15 14 19 -> 19*5 = 19+19+9+15+14+19 (=95)

LEGALIZE -> 12 5 7 1 12 9 26 5 -> 12*5 = 7+1+12+9+26+5 (=60)

• I almost missed it! I thought of it just when you posted it, but I miscalculated twice. Thank god I tried it again :P – Pretzel Sep 24 at 16:46
• Great Work~~~, and both addition & multiplication are commutative :D – Conifers Sep 25 at 1:53
• Yes! Forgot to mention this as the reasoning behind the name :P – Pretzel Sep 25 at 12:19