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APMOPS 2017 Question 21

APMOPS · APMOPS 2017

Question 21

9 natural 3-digit numbers, represented by 9 different letters $a$, $b$, $c$, $d$, $e$, $f$, $p$, $q$ and $r$, formed an addition sequence shown in the diagram below. Find the smallest possible value of $r$.

Source note: the text says that the letters are different, but does not explicitly say that all nine numerical values are different.

Question illustration