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It is proved that for $k\geq 4$, if the points of $k$-dimensional Euclideanspace are coloured in red and blue, then there are either two red pointsdistance one apart or $k+3$ blue collinear points with distance one between anytwo consecutive points. This result is new for $4\leq k\leq 10$.

Equally spaced collinear points in Euclidean Ramsey theory