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It's been a while since I've posted, and in the spirit of my recent works, I've got a simple riddle to get back into the swing of things. As always, I hope you enjoy it, and best of luck!

After the correct answer has been given, I'll update the post with a link to my work that inspired this puzzle.


I'm thinking about adding another row to my display, but I can't remember what the next number is... Perhaps you can help me?

ρ: Prime, ζ: Fibonacci Number, τ: Tribonacci Number

GRID

  • What number should display next?
  • What color should it be?
  • What categories does it fit into?

Thanks for your help!


Hints

The title is a hint.
Hint Image 1

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  • $\begingroup$ It seems that every dot represents a triplet. 2 has the three attributes which helps as a hint. We do not know what is the color though. Is the number displayed - 29? Is this the 100th of the right lower corner? $\endgroup$ – Moti Aug 28 at 1:58
  • $\begingroup$ @Moti The color will make sense with the correct answer. The number displayed is 29 and yes the lower right dot is the 100th digit. I'll be giving a hint on it shortly since it's been a little while since I've posted this. $\endgroup$ – PerpetualJ Aug 28 at 2:03
  • $\begingroup$ I assume same color/size dots represents same number - knowing the number the categories are easy (I think based on the 2). $\endgroup$ – Moti Aug 28 at 2:44
  • $\begingroup$ @Moti that is a safe assumption. :) $\endgroup$ – PerpetualJ Aug 28 at 2:52
  • $\begingroup$ I am guessing - 11pT to display and color green . 101 on the 11th of next line. $\endgroup$ – Moti Aug 28 at 4:58
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Color

The sizes of the circles must matter, right? So let's assign 0 to the smallest circle, 1 to the next smallest, until 9 to the largest. Doing so gives us something like 3141592653... to start. Aha, it's the digits of pi! This is also consistent with the digit displayed: 1 is the 2nd digit (including the 3) in the hint, and 2 is the 29th digit (including the 3). This is also consistent with large numbers displayed.

Categories

Granted I only have a few datapoints here, but it seems like the rule is just to consider which categories that number is in. For instance, 2 is a prime, and also appears in the Fibonacci and Tribonacci sequences. 29 is a prime but not the others; 1 is not a prime but is Fibonacci and Tribonacci.

Therefore, the next dot:

The 101th digit of pi is a 9, so it's a large red dot. 9 is none of the categories so it would not have any categories labeled. The big number is 101 to represent the 101th digit, which is a prime but neither of the other two, so it would get 101ρ.

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  • $\begingroup$ (Just another observation: the title is possibly referring to (rot13) gur fbat jvgu “nzrevpna cvr”) $\endgroup$ – boboquack Aug 29 at 7:47

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