IGO 2022 E5
- Elementary
a) Do there exist four equilateral triangles in the plane such that each two have exactly one vertex in common, and every point in the plane lies on the boundary of at most two of them? b) Do there exist four squares in the plane such that each two have exactly one vertex in common, and every point in the plane lies on the boundary of at most two of them? (Note that in both parts, there is no assumption on the intersection of interior of polygons.)
Proposed by Hesam Rajabzadeh
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
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