In the multiplication given below, all the digits, except one, were consistently replaced by another digit:

    617 
*   702 
_______
   1639 
  3733 
 2807  
__________  
 265699

Find the substitution code and restore the original multiplication.

DECLARE SUB permute (a$)
CLS
a$ = "1234567890": h$ = a$

DO
  IF MID$(a$, 6, 1) <> "0" AND MID$(a$, 7, 1) <> "0" AND MID$(a$, 1, 1) <> "0" AND MID$(a$, 3, 1) <> "0" AND MID$(a$, 2, 1) <> "0" THEN
    mct = 0
    FOR i = 1 TO 9
      IF MID$(a$, i, 1) = LTRIM$(STR$(i)) THEN mct = mct + 1
    NEXT
    IF MID$(a$, 10, 1) = "0" THEN mct = mct + 1
    IF mct = 1 OR mct = 2 THEN
      mpr1 = VAL(MID$(a$, 6, 1) + MID$(a$, 1, 1) + MID$(a$, 7, 1))
      mpr2 = VAL(MID$(a$, 7, 1) + MID$(a$, 10, 1) + MID$(a$, 2, 1))
      prod = mpr1 * mpr2
      pr = VAL(MID$(a$, 2, 1) + MID$(a$, 6, 1) + MID$(a$, 5, 1) + MID$(a$, 6, 1) + MID$(a$, 9, 1) + MID$(a$, 9, 1))
      IF prod = pr THEN
        PRINT mpr1: PRINT mpr2
        PRINT MID$(a$, 1, 1) + MID$(a$, 6, 1) + MID$(a$, 3, 1) + MID$(a$, 9, 1)
        PRINT MID$(a$, 3, 1) + MID$(a$, 7, 1) + MID$(a$, 3, 1) + MID$(a$, 3, 1)
        PRINT MID$(a$, 2, 1) + MID$(a$, 8, 1) + MID$(a$, 10, 1) + MID$(a$, 7, 1)
        PRINT prod: PRINT
      END IF
    END IF
  END IF
  permute a$
LOOP UNTIL a$ = h$

finds these two multiplications (formatted manually):

    516
    693
-------    
   1548
  4644
 3096
-------
 357588

    754
    493
-------    
   5762
  6466
 3894
------- 
 371722
 

where the partial products are done from the code deduced by the multipliers and the products.
 
But manually checking the partial products' values shows that only the first claimed solution is real:

    516
    693
-------    
   1548
  4644
 3096
-------
 357588

 

Posted by Charlie on 2014-03-11 14:30:36