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Decode the double code (Posted on 2011-06-09) Difficulty: 4 of 5
I have multiplied two 3-digit numbers and coded the whole process twice:

In the 1st coding O replaces an odd digit and E the even.
   OOO
 * EOE
  OEOE
  OOO
 OEE  
 OOOEE 
In the 2nd coding S replaces a digit smaller than 6 and B a digit bigger than 5.
   SBB
 * SSB
  SSSB
  SSS
 BSB  
 BBSSB
Try to get my original numbers(digit 9 does not appear in the multiplication) and all other possible solutions, if any.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Not that hard (spoiler) | Comment 5 of 7 |
Well, that difficulty rating looks a little high.  Let's combine to get a single problem

Let a = O and S = 1 or 3 or 5
Let b = O and B = 7  (since 9 is unused)
Let c = E and S = 0, 2 or 4
Let d = E and B = 6 or 8

Then, the problem is

   a77
* cad
------
 acad
 aaa
7cd
------
77acd

well 7 * d ends in a d.
       which can only be 7*8 ends in a 6

Also, 7 * c ends in a d,
        which can only be 7*4 ends in an 8

So, now we have

   a77
* 4a8
------
 aca6
 aaa
7c8
------
77ac6

Well, a77*4 = 7c8, which can only be 177*4 = 708

So, now we have

   177
* 4a8
------
 1416
 aaa
708
------
77ac6

and 177 * a = aaa, which can only be 177*3,

so the only solution is

   177
* 438
------
 1416
 531
708
------
77526
 

Edited on June 13, 2011, 11:40 am
  Posted by Steve Herman on 2011-06-09 20:32:14

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