# What is a Royal Word™?

This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and their spin-off What is a Number™ series.

$$\begin{gather*} % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.0}} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\textbf{Royal Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not Royal Words}^{\;\!™}\Pad\ } \smash{\lower{29px}\bbox[lightblue]{\phantom{\rlap{rubio.2019.05.15}\S{46px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ YOUNG}&\text{ OLD}\\ \hline \text{ FIRE}&\text{ WATER}\\ \hline \text{ COW}&\text{ GOAT}\\ \hline \text{ WORLDBUILDING}&\text{ PUZZLING}\\ \hline \text{ BANANA}&\text{ APPLE}\\ \hline \text{ AUDIO}&\text{ VIDEO}\\ \hline \text{ DECIMAL}&\text{ BINARY}\\ \hline \text{ LAWYER}&\text{ ATTORNEY}\\ \hline \text{ VIOLIN}&\text{ FIDDLE}\\ \hline \text{ MUSHROOM}&\text{ FUNGUS}\\ \hline \hline \end{array} \end{gather*}$$

CSV:

Royal Word™, Not a Royal Word™
YOUNG, OLD
FIRE, WATER
COW, GOAT
WORLDBUILDING, PUZZLING
BANANA, APPLE
AUDIO, VIDEO
DECIMAL, BINARY
LAWYER, ATTORNEY
VIOLIN, FIDDLE
MUSHROOM, FUNGUS


What makes a Royal Word™ a Royal Word™?

Some pairs are synonyms, others are antonyms. Some pairs are completely unrelated. So what is a Royal Word™?

Hint 1:

You can only deduce this with the words in all capitals with no spaces.

Hint 2:

The solution is unrelated to the phonemes of the words and the letter orders of the words.

Hint 3:

The answer can only be found using a method that makes it impossible to deduce the original words without trial and error.

Hint 4:

The answer uses a method that is very difficult to do by hand. Computers will aid you in the process.

Hint 5:

The answer is related to the first digit of the number generated by the method.

Hint 6:

50% of the possible first digits values of the number generated by the method result in Royal Words™, 50% do not.

• Could you please rewrite my words into a table to help the blind? – Galactic Apr 16 '20 at 22:48
• Done :) I’ve put it in a CSV but can put it in one of the fancier Mathjax ones you might have seen in previous questions if needed – Beastly Gerbil Apr 16 '20 at 23:24
• I like a Mathjax to replace my image. – Galactic Apr 16 '20 at 23:32
• Replaced, if someone a lil bit better at Mathjax can fix the blue box that would be much appreciated :) – Beastly Gerbil Apr 17 '20 at 0:00
• "Royal" in trademark?! According to trademarkroom dot com, "Consent can be obtained from the Lord Chamberlain’s office at Buckingham Palace, London, SW1A 1AA" :) That's for the UK only, of course. – Nick Rice May 6 '20 at 8:56

All words depends on:

Hash algorithm SHA-256. If first (in binary) number is 1 -> it is Royal word, otherwise not.
It has 50% chance for every string that first number could be 1, and 50% that it is 0.

For example:

YOUNG is 90008a2bee7e9adbf273a4c637683197878bed1e48a8b8c59ef4e9d95d0069eb, first number is > 7, in binary 1001. So it is Royal
OLD is 099d90cbee62f89e6478e153eb3240efcbe4ac2231bedc3e84549bbeaaba87e8, where 0 in binary is 0000. So it is not Royal
VIDEO is 65b2f9ec331fc7267fd32f75f18e799a3a9217765108226c99b6638ebfb36f84, where 6 in binary is 0110. So it is not Royal

You can check for example here

As a sidenote:

A hint by the author was presumably that SHA resembles the royal title Shah.