# What is a Riven Word™ / Phrase™?

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.

If a word conforms to a special rule, I call it a Riven Word™ or Phrase™.

Use the examples below to find the rule.

$$\begin{array}{|c|c|}\hline \textbf{RIVEN™} & \textbf{UN-RIVEN™}\\\hline \text{ROBE} & \text{COAT}\\\hline \text{AMZN} & \text{MSFT}\\\hline \text{GNAT} & \text{WASP}\\\hline \text{THUG} & \text{RUFFIAN}\\\hline \text{RAVINE} & \text{CREVICE}\\\hline \text{ANGER TAN} & \text{RAGE BURN}\\\hline \text{LIAR ENVY} & \text{TRUE LOVE}\\\hline \text{RINSER FAVE} & \text{AERIE CHURN}\\\hline \text{GENTRY LEG ART} & \text{COMMON ARM TAT}\\\hline \text{RAVER TANGERINE} & \text{RESERVED ORANGE}\\\hline \end{array}$$

CSV version:

RIVEN™,UN-RIVEN™
ROBE,COAT
AMZN,MSFT
GNAT,WASP
THUG,RUFFIAN
RAVINE,CREVICE
ANGER TAN,RAGE BURN
LIAR ENVY,TRUE LOVE
RINSER FAVE, AERIE CHURN
GENTRY LEG ART,COMMON ARM TAT
RAVER TANGERINE,RESERVED ORANGE

• I smell anagrams ... – Rand al'Thor Sep 27 '16 at 18:53
• Tangerine Argentine – greenturtle3141 Sep 27 '16 at 19:28

A Riven word can be defined as:

Any word or phrase which, when ROT13'ed, the result is the same word or phrase, but backwards

Examples:

ROBE = EBOR
... but COAT = PBNG

AMZN = NZMA
... but MSFT = ZFSG

RINSER FAVE = EVAFRE SNIR
... but AERIE CHURN = NREVR PUHEA

RAVER TANGERINE = ENIRE GNATREVAR
... but RESERVED ORANGE = ERFREIRQ BENATR

The reason that each of these words is called a Riven word/phrase is

That "A RIVEN" itself is a Riven phrase:
A RIVEN = N EVIRA

• Hooray! For imaginary bonus points, can you explain the title? – user812786 Sep 29 '16 at 15:39
• @whrrgarbl Just got it and updated the answer :) – Joe Sep 29 '16 at 15:50
• Correct again :) The meaning of "split apart" was just a side effect, it was hard enough already to find sensible words / phrases. – user812786 Sep 29 '16 at 16:17
• Ah, this IS a lot more elegant than what I came up with. I needed to keep working inwards from the ends of the word. – TwoBitOperation Sep 29 '16 at 17:04

For Riven words:

The first pair of letters are the same distance apart in the alphabet as the last pair

EXAMPLES:

ROBE:
RO -> O(PQ)R = 2
BE -> B(CD)E = 2

AMZN:
AM -> A(BCDEFGHIJKL)M = 11
ZN -> N(OPQRSTUVWXY)Z = 11

GNAT:
GN -> G(HIJKLM)N = 6
AT -> T(UVWXYZ)A = 6

THUG:
TH -> H(IJKLMNOPQRS)T= 11
UG -> G(HIJKLMNOPQR)S = 11

RAVINE:
RA: R(STUVWXYZ)A = 8
NE: E(FGHIJKLM)N = 8

LIAR ENVY:
LI: I(JK)L = 2
VY: V(WX)Y = 2

COUNTER-EXAMPLE:

COAT:
CO -> C(DEFGHIJKLMN)O = 11
AT -> T(UVWXYZ)A = 6 or
AT -> A(BCDEFGHIJKLMNOPQRS)18

"COAT" is Un-Riven

• I bet you found this via AMZN. – Rand al'Thor Sep 29 '16 at 14:58
• Yes, that was the key. – TwoBitOperation Sep 29 '16 at 15:02
• So close! You are thinking along the right lines, but there is a simpler (and stricter) explanation. – user812786 Sep 29 '16 at 15:15
• @Joe exactly it! I will add a counterexample to show that vs. this – user812786 Sep 29 '16 at 15:23
• Honestly that probably should have been an answer, not a comment. Fixing that. Anyone reading this, upvote this answer too :) – Joe Sep 29 '16 at 15:24

Not a complete answer, but something I've noticed that might be significant:

We can change the last letter of RIVEN to get RIVER. We can change the other RIVEN™ words and phrases in various ways to get river-related terms:

An anagram of ROBE is BORE, which is a kind of wave that travels upriver

A RAVINE is produced by a river (but a CREVICE is not)

Insert A and O in AMZN and you get AMAZON, which is a river

RAVER can also be transformed into RIVER by changing one letter. As greenturtle3141 has pointed out, TANGERINE is an anagram of ARGENTINE, but none of the major Argentinian rivers seem to fit anything here.

• Liar Envy - swap L to R and anagram to Yin River, in Myanmar – Joe Sep 28 '16 at 15:41
• MSFT (non-Riven) appears to be MISFIT, and the others are just synonyms/antonyms of the Riven word/phrase on the same row (eg. a ruffian is a thug, anger/rage and tan/burn) – Joe Sep 28 '16 at 15:47
• Joe: the synonyms/antonyms thing is typical for this kind of puzzle. Good catch for LIAR ENVY, but it also requires the A to be changed to an I. – paolo Sep 28 '16 at 17:19
• Wow, I'm impressed! ... but you are barking up the wrong tree here. @Joe, the synonym/antonym thing was just a way to think of example non-riven words to put in the chart, and isn't actually relevant to the rule. As a small hint - it was a lot harder to make A Riven Word/Phrase than a non-riven one. – user812786 Sep 28 '16 at 21:50