  The Collision problem is to decide whether a given list of numbers
$(x_1,\ldots,x_n)\in[n]^n$ is $1$-to-$1$ or $2$-to-$1$ when promised one of
them is the case. We show an $n^{\Omega(1)}$ randomised communication lower
bound for the natural two-party version of Collision where Alice holds the
first half of the bits of each $x_i$ and Bob holds the second half. As an
application, we also show a similar lower bound for a weak bit-pigeonhole
search problem, which answers a question of Itsykson and Riazanov (CCC 2021).
