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

If a number conforms to a special rule, I call it a Reversible Number™. If it doesn't, it might be an Irreversible Number™.

Use the following examples below to find the rule.

Reversible number™ Non reversible number™
123 213
348 537
761 879
2485 2639
4762 4519
7249 7564
16983 16938
52769 85372
89572 92134
215743 281397
634927851 564173982

Here is a CSV version:

Reversible number™,Non reversible number™
123,213
348,537
761,879
2485,2639
4762,4519
7249,7564
16983,16938
52769,85372
89572,92134
215743,281397
634927851,564173982

These are not the only examples of Reversible Numbers™ (or Irreversible Numbers™), more can be found.

What rule defines Reversible Numbers™? What separates Reversible Numbers™ and Irreversible Numbers™ from all other numbers?

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    $\begingroup$ "What separates Reversible Numbers™ and Irreversible Numbers™ from all other numbers?" - are you saying Irreversible Numbers™ are not all numbers that aren't Reversible Numbers™? If so, what are an examples of numbers which are both not Reversible™ and not Irreversible™? $\endgroup$
    – boboquack
    Commented Feb 12, 2018 at 22:05
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    $\begingroup$ @boboquack My first hint is probably going to be some numbers that are neither, but for now I can say that, when reversed, a Reversible Number™ will become another Reversible Number™, but an Irreversible Number™ will become neither. $\endgroup$
    – DqwertyC
    Commented Feb 12, 2018 at 22:16

1 Answer 1

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Reversible:

A Reversible Number is one where, when traced on a keypad, no line segment passes through an existing vertex on the path. If the number is flipped, that is still true.

enter image description here

Given the final tracing and the guarantee that it is reversible, you would be able to figure out the original number (or its reverse).

Irreversible:

An Irreversible Number is one where a line segment passes through an existing vertex. This happens when 3 digits are in a line (horizontally, vertically, or diagonally) and it starts in the middle and then goes to each end. (In shorter numbers, this happens immediately; in longer numbers such as the bottom left, it visits another digit in between)

enter image description here

Given the final tracings, you would NOT be able to figure out the original number because there are many possibilities.

Neither:

I imagine a "neither" would be one with the same number repeated, e.g. 5441. No line segment crosses through a vertex; however, you would not be able to figure out that there is more than one 4. Or perhaps another example would be 13, which passes through the 2, but the 2 is not an existing vertex. So it is neither reversible or irreversible

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  • $\begingroup$ Interesting indeed. But it's kind of ruled out by this comment. $\endgroup$
    – ibrahim mahrir
    Commented Feb 12, 2018 at 23:40
  • $\begingroup$ @ibrahimmahrir ah I missed the part about it becoming "neither." Still, I think I am on the right track... unfortunately have to go catch my train now so I'm sure some genius on here will find it before I get another chance! $\endgroup$
    – ferret
    Commented Feb 12, 2018 at 23:44
  • $\begingroup$ @frabjrew You are certainly on the right track! Just not quite there yet :) $\endgroup$
    – DqwertyC
    Commented Feb 13, 2018 at 0:30
  • $\begingroup$ @DqwertyC updated my guess... not completely happy with the "Neither" explanation, but it now fits everything! $\endgroup$
    – ferret
    Commented Feb 13, 2018 at 3:40
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    $\begingroup$ @frabjrew Your last sentence of the neither explanation is essentially right. The puzzle was built around Android phone lockscreens, so a "neither" would be a order that couldn't be a valid lock screen password. $\endgroup$
    – DqwertyC
    Commented Feb 13, 2018 at 3:57

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