2022 USAMO Problems/Problem 2
Revision as of 00:38, 26 March 2022 by Wzs26843545602 (talk | contribs) (Created page with "==Problem== Let <math>b\geq2</math> and <math>w\geq2</math> be fixed integers, and <math>n=b+w</math>. Given are <math>2b</math> identical black rods and <math>2w</math> ident...")
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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
