LOGOLOG
a weblog of wordplay by Eric Harshbarger

## Word Dice

Better late than never.

At my Spring 2010 Puzzle Party I promised to give a special set of dice to the team which scored the highest on a particular puzzle called "Word Dice."

This was a challenge which I had first read about in Ross Eckler's Making The Alphabet Dance. The goal is to arrange 24 different letters of the alphabet onto the sides of four six-sided dice so that you are able to form the most possible 4-letter words from face-up combinations.

The word list of reference I used for this instance of the puzzle was the 4s from the current tournament word list for competitive Scrabble in North America. Several teams submitted answers, but White Team submitted the best answer (as generated by a quickly written script from team member Michael Hollingsworth). Their dice-face configuration of:

```DIE 1: A,O,I,U,X,Z
DIE 2: E,W,B,G,P,C
DIE 3: S,D,Y,V,K,F
DIE 4: T,L,R,M,N,H
```
yielded 715 possible words (there are 4030 valid 4-letter words in the list).

I don't know if this is the best possible answer (I doubt it -- I feel I topped 800 at one point, but lost the answer). But it was good enough for Mike to earn a set of custom dice as pictured below.

And it only took me six months to actually make them.

If any readers out there find a better combination (yielding more words), please let me know!

-- Eric

[29 September 2010]

Archive

There may be 4030 4-letter words in the list but only 3627 can be used as they must be haplograms.

Posted by: Simon Lengyel

Cool problem, very fun to play with.

I found a set yielding 758 words:
Die 1: E, F, G, K, S, Y
Die 2: C, H, L, N, R, V
Die 3: B, D, M, P, T, W
Die 4: A, I, O, U, X, Z

Not sure whether this is the best solution, but it's the one my stochastic hill climber usually finds.

Posted by: Nils Fagerburg

I do not know what word list was used to determine the 4030 "valid" words, yet using the more recent word list of Word Judge Global there can be listed 4392 heterogrammic English words, today. Using this list, the White Team's dice solution can yield 896 words. Nils Fagerburg's set of dice yields a larger set of 942 words.

Posted by: Stuart M. Klimek

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