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Lester's Code

Lester had a secret code where letters are used for digits. Each letter (P, Q, R, S) stands for one (and only one) of these digits: 2, 6, 7, 8.


Question 1: If PQ + PQ + PQ = RRS, which digit does each letter represent?


Question 2: Are other solutions possible if the problem allows the four letters to be any of the digits 0-9?

 


Hint: Write the problem vertically:

PQ
PQ
PQ
____
RRS
Focus on the ones'column...think multiplication.

 


Solution Commentary: With the problem written vertically, the ones column becomes the multiplication problem 3 x Q = **S. Given this new problem, what information do the possible digits tell you...i.e. what are the values of Q and S? Now, focus on P and R.


What was your conclusion for the extension to the full digit range 0-9? Could you use the same basic problem solving strategy as was done for the original problem?