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Let $P_t$ denote the path on $t$ vertices. The $r$-coloured Ramsey number of$P_t$, denoted by $R_r(P_t)$, is the minimum integer $n$ such that whenever thecomplete graph on $n$ vertices is given an $r$-edge-colouring, there exists amonochromatic copy of $P_t$. In this note, we determine $R_r(P_5)$, which isapproximately $3r$.

Multicoloured Ramsey numbers of the path of length four