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)

First off: by inspection Q and Z are not used

GOAD and GROW indicate that A,D are on same cubes as R,W but HOAR tells us that A and R are not on same cube so D is with R and A is with W
GOAD and HOAR indicate that G,D are on same cubes as H,R and since D is with R then G is with H
CHAD and HOAR indicate that C,D are on same cubes as O,R and since D is with R then C is with O

CHAD indicates that C, H, A and D must be on different cubes so we now know the following about the four cubes (I through IV for convenience)

I contains A,W
II contains G,H
III contains C,O
IV contains D,R

Starting with cube III if we eliminate from the alphabet the two unused letters (Q,Z), the six letters we know are on other cubes and all the letters that share words on the list with C or O we are left with seven possible letters (including C and O which we know are on the cube) they are:
C,E,J,N,O,V,X
But since V is in both NAVY and VIBE we can eliminate it because its presence would rule out N and E leaving us with less than six. So cube III is labeled C,E,J,N,O and X.

Consider OPTS and TURN since O and N are both on cube III this tells us that P,S are on same cubes as U,R. but JUMP has both U and P so P is with R (on cube IV) and S is with U. AXIS tells us that S can’t be with A so S,U must be on cube III

Now in the word AXIS A is on I, S is on II, X is on III
Which means I must be on IV (oops confusing nomenclature).

This leaves us with the following info on the cubes
I A,W
II G,H,S,U
III C,E,J,N,O,X
IV D,R,P,I

Now look at cube I eliminating the two non-used letters, the 14 we now know are on other cubes and all the letters that share words on the list with A and W leaves us only six possible letters: A,W,B,L,M,T

In BOUY B is on I, U is on II and O is on III
So Y is on IV

Similarly in MUCK M is on I, U is on II and C is on III so K is on IV. This make six for IV (D,R,P,I,Y,K)

Which leave only F and V to fill the empty two sides of II

Thus the final cubes are as follows

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

Posted by FatBoy on 2003-10-10 10:15:20