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


If a word conforms to a special rule, I call it a range word. Here is a list of range and not-range words:

+-----------+-----------+
|   RANGE   | NOT RANGE |
+-----------+-----------+
| orb       | circle    |
| banjo     | guitar    |
| bamboo    | wood      |
| ear       | mouth     |
| easier    | harder    |
| megahertz | gigahertz |
| haiku     | sudoku    |
| Hindu     | temple    |
+-----------+-----------+

And CSV version:

RANGE,NOT RANGE
orb,circle
banjo,guitar
bamboo,wood
ear,mouth
easier,harder
megahertz,gigahertz
haiku,sudoku
Hindu,temple

QUESTION: What is the rule to tell whether a word is a range word or not?

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A Range Word is a word where:

The first and last letters are exactly 13 letters apart from each other in the English alphabet. In other words, if you apply rot-13 (a Caesar shift of 13 magnitude) to the first letter, you get the last - and vice versa.

Examples:

- orb, banjo, bamboo: B (2nd letter) <--> O (15th letter);
- ear, easier: E (5th letter) <--> R (18th letter);
- megahertz: M (13th letter) <--> Z (26th letter);
- haiku, Hindu: H (8th letter) <--> U (21st letter).

In all cases, count 13 letters on (or back) from the first letter and you arrive at the last letter.

As for the name:

Range itself satisfies this rule, whilst also suggesting some sort of mathematical distance by its definition.

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  • $\begingroup$ Hi Stiv! I've joined this community by seeing this question in the "Hot Network Questions" sidebar. I wonder if you follow a particular procedure to solve such puzzles, or if the starting point in your reasoning is mostly based on experience and instinct? $\endgroup$ – Sylvain Leroux Dec 30 '19 at 13:08
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    $\begingroup$ @SylvainLeroux Hi, and welcome :) A lot of it is experience, to be honest, but here are some key pointers: (i) Check the tags - sometimes these questions contain more than just the usual 'pattern' and 'word-property' tags, which might give you a clue (e.g. arithmetic); (ii) see if any letters appear in the left-hand list but not the right (and vice versa); (iii) check if there are any hidden sequences in the left-hand words (e.g. do they all contain a girls' name? Do they all start with a US state abbreviation?); (iv) if A=1 and Z=26, do the letters add to something interesting? Good luck! :) $\endgroup$ – Stiv Dec 30 '19 at 18:32
  • $\begingroup$ Cool. Thank you @stiv for those explanations! $\endgroup$ – Sylvain Leroux Dec 30 '19 at 19:24
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A range word is

one where the first and last letters are in exact opposite positions in the alphabet (treating it as a circle): in other words, one is the ROT13-encoded version of the other.

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  • $\begingroup$ Do you happen to know of any way I can get push notifications on an Android mobile browser when another user adds an answer during write-up??! Ninja'd again! :) $\endgroup$ – Stiv Dec 30 '19 at 0:38

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