Problem #173: In any $2$-colouring of $\mathbb{R}^2$, for all but at most...

In any $2$-colouring of $\mathbb{R}^2$, for all but at most one triangle $T$, there is a monochromatic congruent copy of $T$.

SOLVED

Problem Statement

In any $2$-colouring of $\mathbb{R}^2$, for all but at most one triangle $T$, there is a monochromatic congruent copy of $T$.

Categories: Geometry Ramsey Theory

Progress

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.

Source: erdosproblems.com/173 | Last verified: January 14, 2026

Problem Statement

Progress

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