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FUZZY

alphametic puzzle

Question

substitute distinct numbers for each letter

 

ADDITION PROBLEM

 

             
        C A S E
        C O P S
      C L O S E
    C O R P S E
    C O L L A R
    C E L L A R
               
               
    R E C T O R

how to solve?

 

             

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To begin with, C must be less than 4, otherwise the sum would have 7 digits. If C is 3, then R is 9 and C+O+O+E < E, which is impossible, so C cannot be 3. This leaves only two options for C (either 1 or 2). If you try C=1 with various values for O, you can prove that C cannot be 1. Repeat with C=2 to find the solution.

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 So you have to assume  c=1 and try 2 to 9 for O? If it is deduced that c=2, then again try all other values for O?

isn't there a shorter and more efficient way of solving?

 

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