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?

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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

Posted by Ady TZIDON on 2008-08-25 15:38:13