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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 :)

bobble
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JKHA
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    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
  • Do you acknowledge the existence of indigo? Seems potentially pertinent, given the question about red. – Ben Barden May 15 '20 at 18:41
  • @BenBarden, I can't believe I missed that... Thanks! – JKHA May 15 '20 at 19:10
  • Is 17 to be orange or yellow? – Jeremy Dover May 15 '20 at 19:14
  • I feel like it should be possible for us to leverage the fact that we have the versions both with and without indigo thanks to the edit history, but I'll admit that I'm still quite lost. Perhaps, when the time comes, you could formalize that as your first clue. :) – Ben Barden May 15 '20 at 21:17
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    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
  • @BenBarden, yes! That could be an idea for a clue. However, I suggest you to focus on the last version – JKHA May 16 '20 at 12:15
  • @athin, I suggest you to focus on the last version. For your notes, I think you can apply them to the current puzzle :) – JKHA May 16 '20 at 12:16
  • Are colors limited to ROY G BIV, or are others (Black, White, Cyan) possible? – dan04 May 18 '20 at 04:08
  • @dan04, maybe I'll answer in the next hint? – JKHA May 18 '20 at 13:41
  • I think it is time for next hint :P – Sagar Chand May 20 '20 at 11:22
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    @dan04, last hint answers your question :) – JKHA May 20 '20 at 13:54
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    @SagarChand, no sooner said than done! – JKHA May 20 '20 at 13:55
  • Got any more of those juicy hints? I'm lost. – XenoDwarf May 27 '20 at 07:13
  • One more hint Please? – Ankit Jun 10 '20 at 01:03
  • @Ankit, a bit late, but done! – JKHA Jun 21 '20 at 21:15
  • In case someone haven't noticed yet, the possible color codes are the rot13(pbybef bs gur envaobj). Unfortunately I don't have much more to post an answer – melfnt Jun 23 '20 at 13:38
  • Are 6 and 17 correct? – the default. Jun 24 '20 at 13:07
  • @mypronounismonicareinstate, I have re-check and you have pointed out the two integers where I made a shift mistake... I apologize. I'm catching up myself that it was unconsciously there to make the puzzle harder :p I think you have solved it, haven't you? – JKHA Jun 24 '20 at 18:06
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    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
  • @boboquack, yes I agree with you. I have totally been sloppy with this puzzle... I apologize to JeremyDover. If you had the answer a month ago, I would feel appropriate to select your answer. – JKHA Jun 25 '20 at 10:53
  • @boboquack me too, I spotted the nice pattern some time ago but that two items didn't match it so I gave up. – melfnt Jun 26 '20 at 14:29

1 Answers1

13

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).

the default.
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