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MathNet 2020 — Math Olympiad Vault — Part 04 Question 82

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 04

Question 82

Consider lattice points of a $6 \times 7$ grid. We start with two points $A$, $B$. We say two points $X$, $Y$ are connected if one can reflect several times with respect to points $A$, $B$ and reach from $X$ to $Y$. What is the minimum number of connected components, over all choices of $A$, $B$?