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?

T * N congr N and A * N congr N lead to N = 5 and T odd.

O + E = O............ E = 0.

R * N congr 0, so R is even, R = 2 or 4 or 6 or 8.

If R = 2...... B = 1.... M = 6...... T = 3 ...... C = 8 ........... no value for A.

If R = 4 ..... B = 2 ..... M = 6 .... T = 3 .... for T*M, M = 9, C = 7........ no value for A.

If R = 6 ..... B = 3 ..... no value for M.

If R = 8 ...... B = 4 ...... M = 6........ T = 7 .......C = 2 .... A = 9 O = 3.... I = 1

                6 0 5

                9 8 7

-------------------

             4 2 3 5 

          4 8 4 0

       5 4 4 5

-------------------

       5 9 7 1 3 5 

Posted by pcbouhid on 2008-08-23 13:27:04