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Cell Choices (Posted on 2013-03-05) Difficulty: 3 of 5
1	8	15	22	29	36	43
2	9	16	23	30	37	44
3	10	17	24	31	38	45
4	11	18	25	32	39	46
5	12	19	26	33	40	47
6	13	20	27	34	41	48
7	14	21	28	35	42	49
In the 7x7 array given above, select six numbers from six cells simultaneously satisfying the following conditions:
  1. No two numbers chosen should belong to the same row;
  2. No two numbers chosen should belong to the same column;
  3. In the set of numbers chosen, each of the ten digits appears once and only once.
For example, if the numbers selected are 7,9,18,26,30 and 45 then this violates the given conditions as 9 and 30 belong to the same row.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 2 of 3 |

DECLARE SUB doCol (col!)
DECLARE FUNCTION gridNo! (row!, col!)
CLEAR , , 25000
DIM SHARED rowused(7), colnotused, nums(7), numstr$
CLS
FOR colnotused = 1 TO 7
   doCol 1
NEXT colnotused

SUB doCol (col)
  IF col <> colnotused THEN
    FOR row = 1 TO 7
      IF rowused(row) = 0 THEN
        s$ = LTRIM$(STR$(gridNo(row, col)))
        IF LEFT$(s$, 1) <> RIGHT$(s$, 1) OR LEN(s$) = 1 THEN good = 1: ELSE good = 0
        FOR i = 1 TO LEN(s$)
          IF INSTR(numstr$, MID$(s$, i, 1)) > 0 THEN good = 0: EXIT FOR
        NEXT
        IF good THEN
          nums(col) = gridNo(row, col)
          savenumstr$ = numstr$
          numstr$ = numstr$ + "," + s$
          rowused(row) = 1
          IF col = 7 THEN
            PRINT numstr$
          ELSE
            doCol col + 1
          END IF
          numstr$ = savenumstr$
          nums(col) = 0
          rowused(row) = 0
        END IF
      END IF
    NEXT
  ELSE
    IF col = 7 THEN
      PRINT numstr$
    ELSE
      doCol col + 1
    END IF
  END IF
END SUB

FUNCTION gridNo (row, col)
 gridNo = (row - 1) MOD 7 + 1 + 7 * (col - 1)
END FUNCTION

finds

6,8,17,25,30,49


  Posted by Charlie on 2013-03-05 15:42:23
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