Monday, September 12, 2022
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cipher – Communication through a Rubik’s dice


I watched The Promised Neverland just lately and after exploring slightly, I discovered that Norman used a 5x5x5 Rubik’s dice (aka a professor’s dice) to speak when he was held on the $Lambdatext{-}7214$ analysis facility. The picture beneath describes the identical.

enter image description here


I started questioning how one may probably use a dice for communication. One thought struck me which concerned utilizing one row to encode one character. Here’s the strategy I devised:

enter image description here

The picture above exhibits a row of a 5x5x5 dice as seen from the entrance.

Here are the numbers related to the six colors that represent the dice:

  • White: 1
  • Blue: 2
  • Orange: 3
  • Green: 4
  • Red: 5
  • Yellow: 6

    It’s onerous for me to elucidate how I got here up with this or why it’s what it’s however I believe stating some examples will provide help to perceive it simply effective.


    Let’s say that the character that we have to encode is on the $x^{mathrm{th}}$ place within the alphabet. Here’s what we have to do to encode it in a row.

    First, we have to see if $xleq24$. If sure, we observe algorithm $A$. If not, we observe algorithm $B$.

    Algorithm $A$:

  • Find $leftlceildfrac x6rightrceil overset{mathrm{def}}{=} y$ the place $lceil krceil$ offers the smallest integer better than or equal to $okay$.
  • Find $x-leftlfloordfrac x6rightrflooroverset{mathrm{def}}{=} z$ the place $lfloor krfloor$ offers the best integer smaller than or equal to $okay$. If $z=0$, make it $6$.
  • Fill the $y^{mathrm{th}}$ sq. from the start with the colour similar to $z$ and fill the final sq. with the color similar to $y$

    We have devised a technique to characterize the primary $24$ alphabets on this approach. The remaining two will likely be coated through Algorithm $B$.

    Algorithm $B$:

  • Paint the final sq. with the color similar to $4+(x-24)=x-20$. So, if $x=25$, paint the final sq. with the colour purple, if it is $26$, paint it with the colour inexperienced.

    Examples:

    If we have to encode $S$, we first discover the worth of $x$ which comes out to be $19$. Also, $y=4$ and $z=1$. $S$ is denoted by:

    enter image description here

    (Black: not related)

    Similarly, the phrase TEST will likely be denoted by:

    enter image description here


    To decrypt a row, let $x$ be the quantity similar to the colour of the rightmost sq. and for $xleq4$, let $y$ be the quantity similar to the $y^{mathrm{th}}$ sq. from the left. If $x>4$, then for $x=5$, the alphabet is $Y$ and for $x=6$, the alphabet is $Z$.

    For $xleq4$, the alphabet is the one on the place $6(x-1)+y$


    What I need to learn about is the potential drawbacks of this technique. One is, clearly that three out of the 5 “squares” in every row are wasted. Another downside is that it is onerous to point out greater than 5 phrases on the entire dice however that does not appear to be an issue with the strategy.

    Also, what are some options to this? What are another methods that you’ve got heard of to perform this and the way do they evaluate with this technique?


    PS: This is my first query on Puzzling SE. So, if I used to be unable to make my technique clear, please let me know in order that I can edit the query for a similar. I do not know if what I speak about is one thing on-topic right here. If it’s and it pursuits individuals and making the query longer is okay, I might very very similar to to elaborate. Edits on the tags are very welcome.

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