# What is the Color Code™?

Inspired from Can you name the country code? and What is a Number™? series

$$\begin{gather} % custom template - reuse if you may \def\S#1#2{\Space{#1}{21px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\color{white}{\textbf{ Number }}}\def\NT{\color{white}{\textbf{ Color Code}^{™}}}\displaystyle \smash{\lower{29px}\bbox[maroon]{\phantom{\rlap{rubio.2020.01.21-custom}\S{6px}{0} \begin{array}{cc}\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\T&\NT\\\hline % ~\text{ 0 }&\color{green}{ Green }\\ \hline ~\text{ 1 }&\color{indigo}{ Indigo }\\ \hline ~\text{ \varphi }&\text{ ? }\\ \hline ~\text{ 2 }&\color{violet}{ Violet }\\ \hline ~\text{ e }&\color{Orange}{ Orange }\\ \hline ~\text{ 3 }&\color{Indigo}{ Indigo }\\ \hline ~\text{ \pi }&\color{Orange}{ Orange }\\ \hline ~\text{ 4 }&\color{red}{ Red }\\ \hline ~\text{ 5 }&\color{orange}{ Orange }\\ \hline ~\text{ 6 }&\color{green}{ Green }\\ \hline ~\text{ 7 }&\color{yellow}{ Yellow }\\ \hline ~\text{ 8 }&\color{green}{ Green }\\ \hline ~\text{ 9 }&\color{Indigo}{ Indigo }\\ \hline ~\text{ 17 }&\color{orange}{ Orange }\\ \hline ~\text{ 42 }&\text{ ? }\\ \hline \end{array}\end{gather}$$

## 3 Questions for this puzzle

1. What is the Color code of $$\varphi$$?
2. What is the Color code of 42?
3. What is the smallest integer number to be $$\color{Blue}{Blue}$$?

# Hint A.1 - 17th May

First reasonable step to resolution is to spell out in English each integer or constant

# Hint B - 20th May

All possible color codes are given in the puzzle

# Hint A.2 - 26th May

Extending hint A.1.

You will need the number of letters of each integer or constant spell out in English.

# Hint C - 21th June

You will need to find the appropriate sort on all colors.

# Hint D - 24th June

I'm adding an hint earlier than I planned as a bounty was given.

The overall cryptography scheme is:

Sort colors like Hint C and select a given number $$x$$.
1. Spell out $$x$$ like Hint A and save the number of letters $$n$$.
2. Apply a cryptography function which needs $$n$$, $$x$$ and the appropriate sort on colors.
3. Output of cryptography function is $$x$$'s color code.

Note that our cryptography function is really simple, in my opinion, nearly all undergraduate students would understand it, but not find it necessarily as you've guessed it :)

• Start points seems like it is a 3 number problem with RGB components. R and G components take only 3 values whereas B only take 2 – Sagar Chand May 15 '20 at 18:04
• Hmm... The puzzle changed a lot from the first time I saw this, didn't it... Should I scrap my old note? Or are both fine as the solving paths are same? – athin May 15 '20 at 21:24
• @dan04, last hint answers your question :) – JKHA May 20 '20 at 13:54
• @SagarChand, no sooner said than done! – JKHA May 20 '20 at 13:55
• I have to say, it's a bit unfortunate that Jeremy Dover might have had the answer a month ago but for the mistake... – boboquack Jun 25 '20 at 10:47

Question 1:

Indigo

Question 2:

Indigo (or, if the hyphen is not counted in the length, Violet).

Question 3:

19

Algorithm used:

Let $$x$$ be the number used, and $$l$$ be its length when written in English (I used "phi" for $$\varphi$$, "pi" for $$\pi$$ and "e" for $$e$$). Then the color is chosen based on $$(\lfloor x \rfloor - l) \bmod 7$$ by indexing into the colors of the rainbow (0 is Red, 1 is Orange, 2 is Yellow and so on).