  In a paper from 1997, Shelah asked whether
$Pr_1(\lambda^+,\lambda^+,\lambda^+,\lambda)$ holds for every inaccessible
cardinal $\lambda$. Here, we prove that an affirmative answer follows from
$\square(\lambda^+)$. Furthermore, we establish that for every pair
$\chi<\kappa$ of regular uncountable cardinals, $\square(\kappa)$ implies
$Pr_1(\kappa,\kappa,\kappa,\chi)$.
