# What is a Richi Word™?

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 Richi Word™.
Use the following examples below to find the rule.

$$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{1}} \def\Title{\textbf{ Richi }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{ CUB }&\text{ BEAR }\\ \hline \text{ AIR }&\text{ WATER }\\ \hline \text{ WEB }&\text{ NET }\\ \hline \text{ MOOD }&\text{ MIND }\\ \hline \text{ MISS }&\text{ FAIL }\\ \hline \text{ PLAY }&\text{ WORK }\\ \hline \text{ NOPE }&\text{ YUP }\\ \hline \text{ GRIND }&\text{ POLISH }\\ \hline \text{ BLACK }&\text{ WHITE }\\ \hline \text{ DECODE }&\text{ ENCODE }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

Richi Words™,Not Richi Words™
CUB,BEAR
AIR,WATER
WEB,NET
MOOD,MIND
MISS,FAIL
PLAY,WORK
NOPE,YUP
GRIND,POLISH
BLACK,WHITE
DECODE,ENCODE


Hint 1:

Hint 2:

Added Language tag here. The title may be applicable, but the rule for Richi Word™ is not.

Hint 3:

$$3n+2-1$$

• I might need a hint for this one – GrumpyLlama59 Nov 4 '19 at 18:06
• @GrumpyLlama59 Here it is :) – Conifers Nov 5 '19 at 14:43
• Does this need the Language tag? – Kyle Williamson Nov 5 '19 at 21:58
• I've had the connection that the hints are pointing to since the puzzle was posted (though surely that should be "ii" rather than "i"?). I just don't know how to use that connection. – Deusovi Nov 8 '19 at 16:47
• I'm in the same boat as @Deusovi I reckon - I know what it's based on, but quite how to derive the numbers I don't know! Still, my last half hour has taught me a lot about symbols I never knew you could make in Unicode! – Stiv Nov 21 '19 at 20:12

Convert the letters in a given word to numbers as A=1, B=2, ..., Z=26, then consider the collection of digits. Then all the Richi words allow you to declare Riichi with those digits; that is, if you add one more digit, you can form one or more melds and exactly one pair, thus forming a winning hand in Mahjong.

A meld is a group of three digits, which is either a triplet (three copies of single digit, e.g. 333) or a sequence (three adjacent digits, e.g. 567). A pair is two copies of single digit, e.g. 11.

Using GRIND as an example: GRIND = 7 18 9 14 4, and sorting the digits gives 1144789. If you add a 1 to the collection, you get 111 44 789 which is one triplet 111, one sequence 789, and a pair 44, which is a winning hand.

I guess I was lucky here because I'm an active Japanese Mahjong player :)

Proof for the given Richi words:

The missing digit from the winning hand is marked in parens.

CUB = 3 21 2 = 123 2(2)
AIR = 1 9 18 = 11 (7)89
WEB = 23 5 2 = 22 3(4)5
MOOD = 13 15 15 4 = 111 (2)34 55 or 111 34(5) 55 or 111 345 5(5)
MISS = 13 9 19 19 = 111 3(3) 999 or 11 1(2)3 999
PLAY = 16 12 1 25 = 111 22 (4)56 or 111 22 56(7)
NOPE = 14 15 16 5 = 111 456 5(5)
GRIND = 7 18 9 14 4 = 11(1) 44 789 or 11 44(4) 789
BLACK = 2 12 1 3 11 = 111 123 2(2) or 11 123 12(3)
DECODE = 4 5 3 15 4 5 = 1(2)3 44 555

Proof for the given non-Richi words:

In order to be a Richi word, a word must give exactly $$3n+2-1$$ digits when converted. Most of the given words do not meet this criteria, except for POLISH and WHITE. I guess WHITE is disqualified because it contains a 0 at T=20 (there's no 0 tile in Mahjong), and POLISH = 16 15 12 9 19 8 = 1111256899 is pretty far from a winning hand.

Connections to the hints:

Hint 1 is a picture of a sparrow (I think). Japanese Mahjong is 麻雀 in Kanji, and 雀 means a sparrow.

Hint 2: Richi (more precisely Riichi/Rīchi) is a Japanese word, though it is a specific term only used in Japanese Mahjong.

Hint 3 is the formula for the number of tiles for a ready hand (where you can declare Riichi). A winning hand has $$3n + 2$$ tiles ($$3n$$ for one or more melds and $$2$$ for the pair), and a ready hand is 1 tile away from that, which is represented as $$-1$$.

• excellent solution!, – ThomasL Oct 6 '20 at 21:16