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 :)

  • 1
    $\begingroup$ 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 $\endgroup$ – Sagar Chand May 15 at 18:04
  • 2
    $\begingroup$ 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? $\endgroup$ – athin May 15 at 21:24
  • 1
    $\begingroup$ @dan04, last hint answers your question :) $\endgroup$ – JKHA May 20 at 13:54
  • 1
    $\begingroup$ @SagarChand, no sooner said than done! $\endgroup$ – JKHA May 20 at 13:55
  • 3
    $\begingroup$ I have to say, it's a bit unfortunate that Jeremy Dover might have had the answer a month ago but for the mistake... $\endgroup$ – boboquack Jun 25 at 10:47

Question 1:


Question 2:

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

Question 3:


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).

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