In this game of Letter Cubes, a different letter of the alphabet is on each face of each of the 4 cubes so that 24 of the 26 letters of the alphabet occur. Words are formed by rearranging and turning the cubes so that the top letters spell a common 4-letter word. The 14 words below have been made using today's cubes.

Can you recover the 6 letters on each?

AXIS
BUOY
CHAD
FAKE
FOIL
GOAD
GROW
HOAR
JUMP
MUCK
NAVY
OPTS
TURN
VIBE

(puzzle originally from www.allstarpuzzles.com)

From CHAD and GOAD we know that C and H share the same two cubes as G and O. From HOAR we see the O and the H must be on different cubes, so H and G share a cube as do C and O.

From CHAD and HOAR, we know C and D share 2 cubes with O and R. Since we know that C shares with O, it follows that D shares with R.

From GOAD and GROW, we see A,D share with R,W, and since D shares with R, A shares with W.

From JUMP and MUCK, we see J,P share with C (along with its O) and K. OPTS tells us that O (and its accompanying C) can't share with P, so P shares with K and J shares with C and O.

Then, using the word OPTS to give starting identities to the four cubes we have:
JCO
PK
T
S

Using the words to indicate which letters can't appear with which others, we can produce a grid, and using the letters that we just found must go with each other to copy information from one row and column to another to fill in blanks, we get a grid like:

  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


A o   x x x x x x x x x     x x x   x x     x o x x


B     x   x       x x         x           x x     x


C x x o x   x x x x o x x x   o x   x x x x   x   x


D x   x o     x x   x       x x     o   x x   x


E x x       x     x   x         x           x x


F x   x   x       x x x x     x x             x


G x   x x     o o   x         x     x         x


H x   x x     o o   x         x     x         x


I x x x   x x       x   x     x       x     x x x


J x x o x   x x x x o x x x   o x   x x x x   x   x


K x   x   x x       x o   x   x o     x x x   x


L     x     x     x x         x


M     x             x x       x x         x


N x     x                           x   x x x x   x


O x x o x   x x x x o x x x   o x   x x x x   x   x


P x   x   x x       x o   x   x o     x x x   x


Q


R x   x o     x x   x       x x     o   x x   x


S x   x           x x x       x x       x     x x


T     x x           x x     x x x   x x   x


U   x x x           x x   x x x x   x   x         x


V x x     x       x         x                 x   x


W o   x x x x x x x x x     x x x   x x     x o x x


X x               x                   x       x


Y x x x             x       x x           x x x


Z

with Q and Z absent because they aren't on the cubes.

The x's indicate they can't be together and the o's that they must be together.

Allowable letters to share with the ones already on our cubes are:
AW: BLMTU
COJ: ENVX
PK: BDGHILNRVXY
S: BDEFGHLMNRSUVY

T appears only on the AW cube, and I only on the PK list, so they must actually be on those respective cubes.

Then TURN prevents U from appearing on what's now the AWT cube.

Then going back through the words one by one, letters can be placed on the appropriate cubes:

AWTLBM
COJXEN
PKIYDR
SFVUHG

Posted by Charlie on 2003-08-17 11:16:21