2022 USAMO Problems/Problem 2
Problem
Let and
be fixed integers, and
. Given are
identical black rods and
identical white rods, each of side length 1.
We assemble a regular gon using these rods so that parallel sides are the same color. Then, a convex
-gon
is formed by translating the black rods, and a convex
-gon
is formed by translating the white rods. An example of one way of doing the assembly when
and
is shown below, as well as the resulting polygons
and
.
Prove that the difference of the areas of and
depends only on the numbers
and
, and not on how the
-gon was assembled.
Solution
[WIP]
See also
2022 USAMO (Problems • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |
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