This is inspired by the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles, and the Number™ series.

If a number conforms to a special rule, I call it a Trinity Number™. Use the examples below to find the rule.

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{1}} \def\Title{\textbf{ Trinity }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Number}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[lightblue]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ 666 }&\text{ 777 }\\ \hline \text{ 1988 }&\text{ 2020 }\\ \hline \text{ 2048 }&\text{ 64 }\\ \hline \text{ 404 }&\text{ 200 }\\ \hline \text{ 4096 }&\text{ 1024 }\\ \hline \text{ 1048576 }&\text{ 2097152 }\\ \hline \text{ 89 }&\text{ 97 }\\ \hline \text{ 20200520 }&\text{ 20201225 }\\ \hline \end{array}$$

The puzzle satisfies the series' inbuilt assumption that each number can be tested for whether it is a Trinity Number™ without relying on the other numbers. These are not the only examples of Trinity Numbers™; many more exist.

What is the special rule these numbers conform to?

CSV version:

Trinity Number™, Not Trinity Number™
666, 777
1988, 2020
2048, 64
404, 200
4096, 1024
1048576, 2097152
89, 97
20200520, 20201225


If you were to write down all of the numbers on paper, one of the Trinity numbers™ will possibly be not found in the set of Trinity Numbers™ (i.e. depending on how it is written, it could become a non-Trinity Number™).

  • $\begingroup$ I like the trademark $\endgroup$ – Ankit May 20 at 18:04

It appears that each Trinity Number™ encloses at least three separate planar regions inside its digits. Depending on font/writing conventions, a '4' can contribute zero or one to this total, and a '0' one or two. If assuming '4'->+1 and '0'->+1, this explains the given lists. '404' would be disqualified if '4's are not enclosed, and slashed '0's would make each NTN containing them ->TN.

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  • 3
    $\begingroup$ Could you illustrate this with a diagram? I'm not sure I follow... Thanks :) $\endgroup$ – Stiv May 21 at 15:44
  • 3
    $\begingroup$ @Stiv, he means count the 'holes' of the digits :) $\endgroup$ – Prim3numbah May 21 at 17:41
  • 3
    $\begingroup$ @Prim3numbah That's infinitely clearer, thanks. 'Planar regions' is not a phrase I've ever come across... $\endgroup$ – Stiv May 21 at 18:37

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