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In this note we give a negative answer to a question proposed byAlmendra-Hern\'andez and Mart\'inez-Sandoval. Let $n\le m$ be positive integersand let $X$ and $Y$ be sets of sizes $n$ and $m$ in $\mathbb R^{n-1}$ such that$X\cup Y$ is in generic position. There is a natural order on $X\times Y$induced by the distances between the corresponding points. The question is ifall possible orders on $X\times Y$ can be obtained in this way. We show thatthe answer is negative when $n<m$. The case $n=m$ remains open.

Total orders realizable as the distances between two sets of points