Puzzle 93 - Solution

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 The question was

In the addition problem below, the digits B and C represent a number different from any of the other numbers shown (that is, not 1, 4, 5, 6, or 9). 
 
  B5  
+C9
-------
 164

What are the only two possible values for B and C?

Solution:

When we add digits on units place, we get 5+9 = 14 and 1 is carried to tens place. 

Ten's place addition will be B+C+1 = 16

B+C = 16-1 = 15

If B and C are unique, the possible solutions are 9,6 or 8,7. As the questions says, 9 and 6 etc. are to be excluded, the possible values for B and C are 8 and 7.
 

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