GeekDad Puzzle of the Week Solution – Letter Dice

Reading Time: 2 minutes

This past week’s puzzle, as previously presented:

This week’s puzzle is a combination of combinatorics and spelling. Imagine a set of dice that bears not pips or numbers, but letters. This set of dice contains two 6-sided dice (hexahedron/cubes), one 8-sided die (octahedron), and one 4-sided die (tetrahedron.)

Each individual die displays the following sets of letters:

wee_hexahedronA, C, E, I, O, Twee_hexahedronA, E, L, R, S, T
wee_octahedronD, H, I, K, L, N, O, Swee_tetrahedronD, E, M, O

Based upon the set of words legal for your favorite crossword-style tile-based boardgame, how many different words can be “rolled” from these dice? Additionally, of the 4-letter words available, are there some words with different (better) odds?

Based upon an official favorite crossword-style tile-based boardgame dictionary, I got the following counts of words “rollable” from the unusual dice detailed above:

2-letter words57
3-letter words307
4-letter words843
total words1,207

The “most rollable” word was OLEO, a colloquial term for margarine. It can be rolled some 6 different ways across the four dice. As the two hexahedrons have “EO,” and “EL,” the octahedron has “LO,” and the tetrahedron has “EO,” we can see:

6-1 (EO)6-2 (EL)4 (EO)8 (LO)
6-1 (EO)8 (LO)6-2 (EL)4 (EO)
8 (LO)6-2 (EL)6-1 (EO)4 (EO)
8 (LO)6-2 (EL)4 (EO)6-1 (EO)
4 (EO)6-2 (EL)6-1 (EO)8 (LO)
4 (EO)8 (LO)6-2 (EL)6-1 (EO)

Congratulations to Randy Slavey for being selected as this week’s winner from among the correct (or reasonably correct) entries submitted. The $50 Gift Certificate from the party animals at ThinkGeek is on its way to him!

Thanks to Randy and everyone else that submitted an entry.

Happy puzzling!

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