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2021 IMO Shortlist
G3
G3
Part of
2021 IMO Shortlist
Problems
(1)
Maximize Sum of Areas in Lattice Grid
Source: 2021 ISL G3
7/12/2022
Consider a
100
×
100
100\times 100
100
×
100
square unit lattice
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(hence
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has
10000
10000
10000
points). Suppose
F
\mathcal{F}
F
is a set of polygons such that all vertices of polygons in
F
\mathcal{F}
F
lie in
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and every point in
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is the vertex of exactly one polygon in
F
.
\mathcal{F}.
F
.
Find the maximum possible sum of the areas of the polygons in
F
.
\mathcal{F}.
F
.
Michael Ren and Ankan Bhattacharya, USA