## Word Cube

### July 13, 2010

Word cube is game in which players form words from the nine letters in a cube. Words must have four or more letters and must use the central letter from the cube; at least one word will use all nine letters in the cube. The player who forms the most words wins. Many newspapers publish a word cube on their puzzle page, and Stealthcopter publishes a word cube on line daily. Wikipedia describes word cubes under the caption “word polygon.” There are twelve words formed from the word cube at right: bonnie, bunion, coin, concubine, conic, cubic, ennui, icon, nice, nine, nuncio, and union.

Your task is to write a program that finds all matching words for a given word cube. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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### 13 Responses to “Word Cube”

1. [...] Praxis – Word Cube By Remco Niemeijer In today’s Programming Praxis exercise our task is to write a program to solve Word Cube puzzles, in which you [...]

2. Remco Niemeijer said

```import Data.Char
import Data.List

solve :: String -> [String] -> [String]
solve c = filter (\w -> length w > 3 && elem (c !! 4) w && null (w \\ c))

wordcube :: String -> IO ()
wordcube cube = mapM_ putStrLn . solve cube .
lines . map toLower =<< readFile "words.txt"
```
3. karijes said

Here is my attempt in clojure:

4. matÃ­as said

A bit of python:

def words_in_cube(cube):
return filter(lambda word: 3 < len(word) < 10 and \
cube[4] in word and
all(word.count(x) <= cube.count(x) for x in word),

5. Gary Johnson said
```;; My clojure solution.
;; The previous one forgets to compare the distribution
;; of characters between the words from the word list
;; and the characters from the word cube.

(ns wordcube

(defn count-chars [chars] (apply merge-with + (for [char chars] {char 1})))

(defn solve [chars words-file]
(let [middle-char #{(get chars 4)}
char-counts (count-chars chars)]
(filter #(and (> (count %) 3)
(some middle-char %)
(every? (fn [[char reps]] (<= reps (char-counts char 0))) (count-chars %)))

;; Usage
(solve "ncbcioune" "words.txt")
```
6. Mac said

Here’s a version in LUA:

http://pastebin.com/vBeDvup9

@matias: The python version misses the words with upper case characters.

7. [...] is my first solution for a Programming Praxis assignment, the Word Cube [...]

8. Jebb said

I’d appreciate any well-versed criticism of the regex I used:

```def cubewords(word_cube):
import re
center = word_cube[4]
f = open('/usr/share/dict/words', 'r')
f.close()
pattern1 = "(?mi)(?=^\w{4,}\$)(?=^[" + word_cube + "]+\$)^\w*" + center + "\w*\$"
return re.findall(pattern1, str)
```
9. Gary Johnson said

@Jebb

The character set match ^[ncbcioune]+\$ just validates that your dictionary word only consists of characters from the cube. However, like some of the other answers here, it doesn’t account for the distribution of these characters in the cube and the dictionary word. Therefore, your algorithm gives incorrect answers like “bobbin”, “innocence”, “niece”, and “onion”.

10. [...] that finds all matching words for a given word cube. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments [...]

11. Jebb said

@ Gary: OK, looks like I’d completely misunderstood the assignment. I’m beginning to suspect regexes are not the right tool here…

12. [...] in my recent set of Word Games from Programming Praxis, today we’re tasked with finding all words made from a grid of [...]

13. JP said

Here’s a version written in Racket that generalizes to any size grid (although the minimum length of 4 is hard-coded) and seems to work pretty well:
Word Cubes