In this game of Letter Cubes, each word of one to four letters in uppercase below are used. Except for the letters "Q" and "X", a different letter of the alphabet is on each face of each of the four cubes.

Can you identify the six letters on each cube?

FOR EACH WORD A CUBE IS USED JUST ONCE:
FORM, GAZE, HACK, HOLE, LAZY, LIMP, SING AND VENT

The below program is able to solve the puzzle even with the information from HACK, VENT and AND missing (by overlaying with one of the other words, which provides no more information than that word appearing only once). It just goes faster if HACK, LAZY and AND are in fact used.  There are probably alternate sets of words that could have been left out and still had a solvable puzzle.

The program:

DECLARE SUB addIn (lvl!)
DATA FOR, EACH, WORD, A, CUBE, IS, USED, JUST, ONCE
DATA FORM, GAZE, VENT, HOLE, VENT, LIMP, SING, VENT, VENT

REM  FOR, EACH, WORD, A, CUBE, IS, USED, JUST, ONCE
REM  FORM, GAZE, HACK, HOLE, LAZY, LIMP, SING, AND , VENT

 

CLEAR , , 9999

DIM SHARED USED(26), hist(24)

USED(17) = 1: USED(24) = 1
hist(1) = 1: USED(1) = 1

 

DIM w$(18)
FOR i = 1 TO 18
 READ w$(i)
NEXT

DIM SHARED grid(26, 26)

FOR wd = 1 TO 18
 FOR l1 = 1 TO LEN(w$(wd)) - 1
  FOR l2 = l1 + 1 TO LEN(w$(wd))
   lt1$ = MID$(w$(wd), l1, 1)
   lt2$ = MID$(w$(wd), l2, 1)
   IF lt2$ < lt1$ THEN SWAP lt1$, lt2$
   ltr1 = INSTR("ABCDEFGHIJKLMNOPQRSTUVWXYZ", lt1$)
   ltr2 = INSTR("ABCDEFGHIJKLMNOPQRSTUVWXYZ", lt2$)
   grid(ltr1, ltr2) = 1
   grid(ltr2, ltr1) = 1
  NEXT
 NEXT
NEXT
  PRINT " 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"
  FOR i = 1 TO 26
   PRINT MID$("ABCDEFGHIJKLMNOPQRSTUVWXYZ", i, 1);
   FOR j = 1 TO 26

    IF i = j THEN
     PRINT "\ ";
    ELSE
     IF grid(i, j) THEN
      PRINT "x ";
     ELSE
      PRINT ". ";
     END IF
    END IF
   NEXT
   PRINT
  NEXT

addIn 2

SUB addIn (lvl)
 IF lvl MOD 6 = 1 THEN
   FOR i = 1 TO 26
     IF USED(i) = 0 THEN
       USED(i) = 1
       hist(lvl) = i
       GOSUB checkIt
       USED(i) = 0
       EXIT FOR
     END IF
   NEXT
 ELSE
   FOR i = hist(lvl - 1) + 1 TO 26
     IF USED(i) = 0 THEN
       kMin = ((lvl - 1) \ 6) * 6 + 1
       good = 1
       FOR k = kMin TO lvl - 1
        h1 = hist(k): h2 = i
        IF h2 < h1 THEN SWAP h1, h2
        IF grid(h1, h2) <> 0 THEN good = 0
       NEXT
       IF good THEN
         USED(i) = 1
         hist(lvl) = i
         GOSUB checkIt
         USED(i) = 0
       END IF
     END IF
   NEXT
 END IF

EXIT SUB

checkIt:
  IF lvl = 24 THEN
   FOR j = 1 TO 24
     PRINT MID$("ABCDEFGHIJKLMNOPQRSTUVWXYZ", hist(j), 1);
     IF j MOD 6 = 0 THEN PRINT "|";
   NEXT
   PRINT
  ELSE
   addIn lvl + 1
  END IF
RETURN

END SUB

finds a letter grid of letter pairs found within the same words (not necessarily adjacent):

 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\ . x . x . x x . . . . . . . . . . . . . . . . . x
B. \ x . x . . . . . . . . . . . . . . . x . . . . .
Cx x \ . x . . x . . . . . x x . . . . . x . . . . .
D. . . \ x . . . . . . . . . x . . x x . x . x . . .
Ex x x x \ . x x . . . x . x x . . . x x x x . . . x
F. . . . . \ . . . . . . x . x . . x . . . . . . . .
Gx . . . x . \ . x . . . . x . . . . x . . . . . . x
Hx . x . x . . \ . . . x . . x . . . . . . . . . . .
I. . . . . . x . \ . . x x x . x . . x . . . . . . .
J. . . . . . . . . \ . . . . . . . . x x x . . . . .
K. . . . . . . . . . \ . . . . . . . . . . . . . . .
L. . . . x . . x x . . \ x . x x . . . . . . . . . .
M. . . . . x . . x . . x \ . x x . x . . . . . . . .
N. . x . x . x . x . . . . \ x . . . x x . x . . . .
O. . x x x x . x . . . x x x \ . . x . . . . x . . .
P. . . . . . . . x . . x x . . \ . . . . . . . . . .
Q. . . . . . . . . . . . . . . . \ . . . . . . . . .
R. . . x . x . . . . . . x . x . . \ . . . . x . . .
S. . . x x . x . x x . . . x . . . . \ x x . . . . .
T. . . . x . . . . x . . . x . . . . x \ x x . . . .
U. x x x x . . . . x . . . . . . . . x x \ . . . . .
V. . . . x . . . . . . . . x . . . . . x . \ . . . .
W. . . x . . . . . . . . . . x . . x . . . . \ . . .
X. . . . . . . . . . . . . . . . . . . . . . . \ . .
Y. . . . . . . . . . . . . . . . . . . . . . . . \ .
Zx . . . x . x . . . . . . . . . . . . . . . . . . \

or, if all the words were counted:

 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\ . x x x . x x . . x x . x . . . . . . . . . . x x
B. \ x . x . . . . . . . . . . . . . . . x . . . . .
Cx x \ . x . . x . . x . . x x . . . . . x . . . . .
Dx . . \ x . . . . . . . . x x . . x x . x . x . . .
Ex x x x \ . x x . . . x . x x . . . x x x x . . . x
F. . . . . \ . . . . . . x . x . . x . . . . . . . .
Gx . . . x . \ . x . . . . x . . . . x . . . . . . x
Hx . x . x . . \ . . x x . . x . . . . . . . . . . .
I. . . . . . x . \ . . x x x . x . . x . . . . . . .
J. . . . . . . . . \ . . . . . . . . x x x . . . . .
Kx . x . . . . x . . \ . . . . . . . . . . . . . . .
Lx . . . x . . x x . . \ x . x x . . . . . . . . x x
M. . . . . x . . x . . x \ . x x . x . . . . . . . .
Nx . x x x . x . x . . . . \ x . . . x x . x . . . .
O. . x x x x . x . . . x x x \ . . x . . . . x . . .
P. . . . . . . . x . . x x . . \ . . . . . . . . . .
Q. . . . . . . . . . . . . . . . \ . . . . . . . . .
R. . . x . x . . . . . . x . x . . \ . . . . x . . .
S. . . x x . x . x x . . . x . . . . \ x x . . . . .
T. . . . x . . . . x . . . x . . . . x \ x x . . . .
U. x x x x . . . . x . . . . . . . . x x \ . . . . .
V. . . . x . . . . . . . . x . . . . . x . \ . . . .
W. . . x . . . . . . . . . . x . . x . . . . \ . . .
X. . . . . . . . . . . . . . . . . . . . . . . \ . .
Yx . . . . . . . . . . x . . . . . . . . . . . . \ x
Zx . . . x . x . . . . x . . . . . . . . . . . . x \

(see C vs K, for example, or A vs N)

but either way, the solution is found as:

ABOPSV|CDFGLT|EIJKRY|HMNUWZ|

as being the four cubes.

Posted by Charlie on 2006-06-28 14:09:10