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OPEN This is open, and cannot be resolved with a finite computation.
In any $2$-colouring of $\mathbb{R}^2$, for all but at most one triangle $T$, there is a monochromatic congruent copy of $T$.
For some colourings a single equilateral triangle has to be excluded, considering the colouring by alternating strips. Shader [Sh76] has proved this is true if we just consider a single right-angled triangle.
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This page was last edited 16 October 2025. (View history) (View the LaTeX source)

When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #173, https://www.erdosproblems.com/173, accessed 2026-09-02

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