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
Not that hard (spoiler)
