Substitute each letter by a different digit from 0 to 9 to satisfy this alphametic multiplication problem, where X represents the multiplication symbol.
M E N
X A R T
B C O N
B R B E
N B B N
N A T I O N
Note: While a solution is trivial with the aid of a computer program, can you derive it without one?
This is a nice problem if offered to be solved
with no calculator no pen and no paper, which I did.
As a fact it is easier done that explained.
1st glance: E è0, Nè5 A,B,R,T,è NEITHER ZERO NOR ONE
2nd glance: since NBBN is a multiple of 11 so is MEN
Therefore M è6 & MENè605
BRBE also is a multiple of 11 so B+B=R and A=R+1 ( A=B+B+carry)
3rd glance and solution: A is ODD but not 1 nor 5 (taken by N) NOR 7 (if it were 7 thern Rè6 while 6 is M NOR 3(1885 has no NBBN pattern)
Ergo Aè9 Rè8 and Tè7(1885 has no BCON pattern)
We now have a solution : 605*987 and glance one more time to see the partial products and the sum Iè1.