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

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B C O N

B R B E

N B B N

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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?

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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.

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1^{st} glance: E è0, Nè5 A,B,R,T,è NEITHER ZERO NOR ONE

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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)

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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.

It fits