In the multiplication given below, all the digits, except one, were consistently
replaced by another digit:
617
* 702
_______
1639
3733
2807
__________
265699
Find the substitution code and restore the original multiplication.
I needed to change to letters. Numbers was too confusing:
ABC
* CDE
_______
BAFG
FCFF
EHDC
_______
EAIAGG
C must be 1, 5, or 6 from the 3rd partial product C*C ends in C but C cannot be 1 or 5 (all partial products have different last digits) so C=6.
C+F= 9 or 10 from fourth column sum, but since F=3 would not carry F=4. Hence G=8.
E*6 ends in 8, since 8 is taken, E=3.
Now consider the first partial product we now have
AB6 * 3 = BA48, to make B6*3 end in 48 it must be
B=1,
since there's no carry, A*3 = 1A so
A=5Dividing from the second partial product 4644/516=
9=D
For the 3rd column sum
I=7And for the 2nd column sum
H=0I don't care to work out the puzzles replacements except to say 1 is not replaced. The corrected multiplication is
516
* 693
_______
1548
4644
3096
__________
357588
I was hoping the fact that only one digit was not replaced would be a vital piece of information. That would have required some interesting logic. But it is not.
Edited on March 11, 2014, 12:40 pm
2nd edit for formatting
Edited on March 11, 2014, 2:42 pm

Posted by Jer
on 20140311 12:21:11 