  In a 2021 paper, Vladimir Tkachuk asked whether there is a non-separable LOTS
$X$ such that $X^2\setminus\{\langle x,x\rangle\colon x\in X\}$ is functionally
countable. In this paper we prove that such a space, if it exists, must be an
Aronszajn line and admits a $\leq 2$-to-$1$ retraction to a subspace that is a
Suslin line. After this, assuming the existence of a Suslin line, we prove that
there is Suslin line that is functionally countable. Finally, we present an
example of a functionally countable Suslin line $L$ such that
$L^2\setminus\{\langle x,x\rangle\colon x\in L\}$ is not functionally
countable.
