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 Decode the double code (Posted on 2011-06-09)
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.

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
------
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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