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.

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**