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Fill in the Blanks (Posted on 2004-07-18) Difficulty: 3 of 5
Make the following equation correct by filling the blanks with the digits 0-9 (the 7 and 5 have been already placed for you):
 7     _ _     _ _
─── = ───── + ─────
 _     _ _     _ 5

See The Solution Submitted by Aaron    
Rating: 2.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer brute force (spoiler present)... | Comment 1 of 6

... finds:

7      =      39      +     60
2             18            45

using:

DECLARE SUB permute (a$)
DEFDBL A-Z
CLS
a$ = "01234689": h$ = a$
n1 = 7
DO
  d1 = VAL(MID$(a$, 1, 1))
  n2 = VAL(MID$(a$, 2, 2))
  d2 = VAL(MID$(a$, 4, 2))
  n3 = VAL(MID$(a$, 6, 2))
  d3 = VAL(MID$(a$, 8, 1) + "5")
  dTot = d2 * d3 ' too lazy to put in LCM routine
  nTot = n2 * d3 + n3 * d2 
  IF d1 * nTot = n1 * dTot THEN ' cross-multiply
   PRINT n1, n2, n3
   PRINT d1, d2, d3
  END IF
  permute a$
LOOP UNTIL a$ = h$

where the subroutine permute has been shown elsewhere on the site.


  Posted by Charlie on 2004-07-18 10:53:03
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