In the 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, including J, 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 the cubes.

CAVE
CLEF
DUPE
FARE
FLUB
GREW
HAZY
KITH
LOIN
POEM
RASP
SMUG
TIRE
VARY

Can you recover the 6 letters on each?

(puzzle originally from www.allstarpuzzles.com)

(In reply to re: Solution by Gamer)

23 letters appear in clue words. J is stipulated. This eliminates Q & X.

From FARE, we know that the three most frequent letters {E,R,A} must be on seperate cubes.

Assign E to cube 1. Eliminate {A,C,D,F,G,I,L,M,O,P,R,T,U,V,W} since they all share a word with E, leaving 5 of {B,H,J,K,N,S,Y,Z} as contenders for cube 1. From HAZY, since A stands eliminated, 1 of {H,Y,Z} is a contender. Hence 4 of {B,J,K,N,S} are contenders.

Assign R to cube 2. Eliminate {A,F,G,I,P,S,T,V,W,Y}, leaving 5 of {B,C,D,H,J,K,L,M,N,O,U,Z} as contenders for cube 2. From FLUB, since F stands eliminated, 1 of {B,L,U} is a contender; from HAZY, since {A,Y} stand eliminated, 1 of {H,Z} is a contender; from POEM, since {P,E} stand eliminated, 1 of {O,M} is a contender. Hence 2 of {C,D,J,K,N} are contenders.

Assign A to cube 3. Eliminate {C,F,H,P,S,V,Y,Z}, leaving 5 of {B,D,G,I,J,K,L,M,N,O,T,U,W} as contenders for cube 3. From FLUB, GREW, LOIN and POEM we get 1 each of {B,U},{G,W},{I,K} and {M.O} as contenders, leaving 1 of {D,J,N} as contender.

Finally, {F,P,V} occupy cube 4, the only cube left for them to occupy, eliminating {B,C,D,L,M,O,S,U,Y) and leaving 3 of {G,H,I,J,K,N,T,W,Z} as contenders for cube 4. From GREW and KITH we get 1 each from (G,W} and {H,I,K,T} as contenders, leaving 1 of (J,N,Z} as contender.

Here on, through an iteration of letters occupying the only cube left to occupy, in turn eliminating other letters from certain cubes, in turn those letters occupying the only cube left to occupy and so on, all other letters fall into place.

Posted by Sanjay on 2003-06-19 14:16:57