See the example below. Using only 1īs and 9īs, the 3x3 grid is filled so the 6 three-digit numbers so formed (in the 3 rows and 3 columns) are in the ascending order shown by the numbers around the grid:

      3   1   6
    +---+---+---+
  2 | 1 | 1 | 9 |
    +---+---+---+
  5 | 9 | 1 | 9 |
    +---+---+---+
  4 | 9 | 1 | 1 |
    +---+---+---+

That is, the 1st is in the 2nd column (111), the 2nd is in the 1st row (119), the 3rd is in the 1st column (199), and so on.

Do the same with these three 4x4 grids.

      3   7   6   4         3   2   8   5         2   4   5   6
    +---+---+---+---+     +---+---+---+---+     +---+---+---+---+
  5 |   |   |   |   |   1 |   |   |   |   |   1 |   |   |   |   |
    +---+---+---+---+     +---+---+---+---+     +---+---+---+---+
  2 |   |   |   |   |   7 |   |   |   |   |   7 |   |   |   |   |
    +---+---+---+---+     +---+---+---+---+     +---+---+---+---+
  8 |   |   |   |   |   6 |   |   |   |   |   3 |   |   |   |   |
    +---+---+---+---+     +---+---+---+---+     +---+---+---+---+
  1 |   |   |   |   |   4 |   |   |   |   |   8 |   |   |   |   |
    +---+---+---+---+     +---+---+---+---+     +---+---+---+---+

1991     1199     1199
1119     9991     9919
9911     9191     1991
1111     1999     9991

from

DECLARE SUB choose (r!, c!)
CLEAR , , 25000
DIM SHARED g(4, 4), n(8), p(8), cta, ctb, ctc

choose 1, 1
PRINT cta, ctb, ctc

END

SUB choose (r, c)
 
 FOR i = 1 TO 9 STEP 8
   g(r, c) = i
   IF r = 4 AND c = 4 THEN
     n(1) = g(1, 1) * 1000 + g(1, 2) * 100 + g(1, 3) * 10 + g(1, 4): p(1) = 1
     n(2) = g(2, 1) * 1000 + g(2, 2) * 100 + g(2, 3) * 10 + g(2, 4): p(2) = 2
     n(3) = g(3, 1) * 1000 + g(3, 2) * 100 + g(3, 3) * 10 + g(3, 4): p(3) = 3
     n(4) = g(4, 1) * 1000 + g(4, 2) * 100 + g(4, 3) * 10 + g(4, 4): p(4) = 4
     n(5) = g(1, 1) * 1000 + g(2, 1) * 100 + g(3, 1) * 10 + g(4, 1): p(5) = 5
     n(6) = g(1, 2) * 1000 + g(2, 2) * 100 + g(3, 2) * 10 + g(4, 2): p(6) = 6
     n(7) = g(1, 3) * 1000 + g(2, 3) * 100 + g(3, 3) * 10 + g(4, 3): p(7) = 7
     n(8) = g(1, 4) * 1000 + g(2, 4) * 100 + g(3, 4) * 10 + g(4, 4): p(8) = 8
     n1 = n(1): n2 = n(2): n3 = n(3): n4 = n(4)
     DO
      done = 1
      FOR k = 1 TO 7
        IF n(k) > n(k + 1) THEN SWAP n(k), n(k + 1): SWAP p(k), p(k + 1): done = 0
      NEXT
     LOOP UNTIL done
     good = 1
     FOR k = 1 TO 7
      IF n(k) = n(k + 1) THEN good = 0: EXIT FOR
     NEXT
     IF good THEN
       s$ = ""
       FOR k = 1 TO 8
         s$ = s$ + LTRIM$(STR$(p(k)))
       NEXT
       IF s$ = "42581763" THEN
         PRINT "A"
         PRINT n1: PRINT n2: PRINT n3: PRINT n4
         PRINT
         cta = cta + 1
       END IF
       IF s$ = "16548327" THEN
         PRINT "B"
         PRINT n1: PRINT n2: PRINT n3: PRINT n4
         PRINT
         ctb = ctb + 1
       END IF
       IF s$ = "15367824" THEN
         PRINT "C"
         PRINT n1: PRINT n2: PRINT n3: PRINT n4
         PRINT
         ctc = ctc + 1
       END IF
     END IF
   ELSE
     col = c + 1
     row = r
     IF col > 4 THEN col = 1: row = row + 1
     choose row, col
   END IF
 NEXT i
END SUB

 

Posted by Charlie on 2008-12-03 18:20:24