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Each letter represents a different digit in this summation. The smallest value of M + O + N + E + Y is ...


The answer is 13.

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1 solution

Duc Anh
Aug 1, 2014
  • M is 1 since MO = S+M (maybe +1 from A+O), since S and M is different digits so M is max =1.
  • O is 0 since it cannot be 1 and 1O = S+1 (maybe +1 from A+O).
  • Now it becomes 9AVE + 10RE = 10NEY.
  • Y is even so it can be 4,6,8,10 (digits 1 and 0 already exists so eliminated this case), (1)2, (1)4, (1)6.
  • Y =4 => E =2 => V+R =12 (since digit 1 already exists) => V,R = {5,7} => A+1 = N. We eliminate all possible answers.
  • continue with Y=6,8,12,14,16 we can easily eliminate most of them but Y =2, E=6, V+R =15 => V,R ={7,8}, A=3, N=4 or A=4,N=5
  • We choose the smallest possible value and have 9376+1086 = 10462.
  • Answer = 13

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