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At Least Three Difference (Posted on 2010-08-04) Difficulty: 3 of 5
Place the numbers 1-9 in the boxes so that the difference of each pair of numbers joined by a line is at least three. The number 8 has already been placed.



No Solution Yet Submitted by Brian Smith    
Rating: 5.0000 (1 votes)

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Solution Computer solution: not just for 8 | Comment 2 of 13 |

The puzzle is solvable even when the 8 is replaced by 1, 2, 4 or 6. The solution to the current puzzle (i.e., with 8 at upper left) is the last pair below. Solutions come in pairs as the second and third numbers in the middle row can always be interchanged.

 1  8  3
 7  2  5
 4  9  6
 1  8  3
 7  5  2
 4  9  6
 2  7  3
 8  1  4
 5  9  6
 2  7  3
 8  4  1
 5  9  6
 4  8  3
 7  2  5
 1  9  6
 4  8  3
 7  5  2
 1  9  6
 6  2  7
 3  5  8
 9  1  4
 6  2  7
 3  8  5
 9  1  4
 8  3  7
 2  6  9
 5  1  4
 8  3  7
 2  9  6
 5  1  4
DECLARE SUB addOn (p!)
DATA 247,1563,289
DATA 17,268,258
DATA 418,75639,83
CLS
DIM SHARED con$(9), numval(9)
FOR i = 1 TO 9
   READ con$(i): PRINT con$(i); "."
NEXT
DIM SHARED used(9)
FOR n = 1 TO 8
used(n) = 1
numval(1) = n
addOn 2
used(n) = 0
NEXT

SUB addOn (p)
 FOR n = 1 TO 9
   IF used(n) = 0 THEN
     good = 1
     FOR j = 1 TO LEN(con$(p))
       psn = VAL(MID$(con$(p), j, 1))
       IF psn < p THEN
         IF ABS(numval(psn) - n) < 3 THEN good = 0: EXIT FOR
       END IF
     NEXT
     IF good THEN
       numval(p) = n
       used(n) = 1
       IF p < 9 THEN
          addOn p + 1
        ELSE
          PRINT numval(1); numval(2); numval(3)
          PRINT numval(4); numval(5); numval(6)
          PRINT numval(7); numval(8); numval(9)
          PRINT
       END IF
       used(n) = 0
     END IF
   END IF
 NEXT
END SUB
 

  Posted by Charlie on 2010-08-04 13:56:24
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