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IMAS 2020–2021 Junior Round 2 Question 10

IMAS · IMAS 2020–2021 Junior Round 2

Question 10

In the diagram, fill each of the “○” with numbers so that the sum of the four vertices of all squares that can be found are equal. If the middle number is filled as $\frac nm$, where $m$ and $n$ are both positive numbers that are relatively prime. What is the value of $m+n$?

Question illustration