Cube 1: A D L M T W
Cube 2: B E K N S Y
Cube 3: C H J O R U
Cube 4: F G I P V Z
According to the introduction, each of the 24 faces of the Letter Cubes has a different letter on it.
Given the word CAVE, we arbitrarily assign C to cube 1, A to cube 2, V to cube 3, and E to cube 4.
C
A
V
E
From the word FARE, F can't be on cube 2 with A or cube 4 with E; and from the word CLEF, F isn't on cube 1 with C. F is on cube 3 with V.
C
A
V F
E
The R in FARE then must be on cube 1 with C, and the L in CLEF must be on cube 2 with A.
C R
A L
V F
E
From VARY, the Y is on cube 4.
C R
A L
V F
E Y
From FLUB, the letter U can't be on cube 2 with L or on 3 with F.
From DUPE, the U also can't be on cube 4 with EY, so the U is on cube 1 with CR.
C R U
A L
V F
E Y
Then in FLUB, the B comes from cube 4.
C R U
A L
V F
E Y B
The P in DUPE isn't on cube 1 with U or cube 4 with E, and from RASP the P isn't on cube 2 with A.
The P is on one face of cube 3.
C R U
A L
V F P
E Y B
In DUPE, then, the D must be on cube 2; and in RASP, the S must be on cube 4.
C R U
A L D
V F P
E Y B S
From POEM, the M isn't on cube 3 with P or cube 4 with E; nor from the word SMUG is the M on cube 1 with U.
The M is on cube 2.
C R U
A L D M
V F P
E Y B S
The O in POEM is on cube 1, and the G in SMUG is on cube 3.
C R U O
A L D M
V F P G
E Y B S
The W in GREW must be on a face of cube 2.
C R U O
A L D M W
V F P G
E Y B S
The I in LOIN isn't on cube 1 (O) or cube 2 (L), while the I in TIRE isn't on cube 4 (E).
I is a letter on cube 3.
C R U O
A L D M W
V F P G I
E Y B S
Therefore, the N in LOIN is on cube 4; and the T in TIRE is the sixth letter on cube 2.
C R U O
A L D M W T
V F P G I
E Y B S N
From KITH, the H isn't on cube 2 with T or cube 3 with I.
From HAZY, H also isn't on cube 4 with Y.
H is on cube 1.
C R U O H
A L D M W T
V F P G I
E Y B S N
In KITH, the K completes cube 4; and in HAZY, the Z is the last letter on cube 3.
C R U O H
A L D M W T
V F P G I Z
E Y B S N K
By elimination, the letter J (from the introduction) must go on cube 1:
C R U O H J
A L D M W T
V F P G I Z
E Y B S N K
And just to rearrange these into alphabetical order:
A D L M T W
B E K N S Y
C H J O R U
F G I P V Z
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