At some intuitive level this problem reminded me of other very different puzzles like [1] and prompted me to wonder if as a general rule the best tactic when on

At some intuitive level this problem reminded me of other very different puzzles like [1] and prompted me to wonder if as a general rule the best tactic when one is faced by a riddle that appears impossible, is to try to think of solutions that involve self reference. It also makes me wonder if the brain at a basal unconscious level uses something analogous to the linked list like solution described here to quickly explore permutation space. 1 https://en.m.wikipedia.org/wiki/Knights_and_Knaves https://en.m.wikipedia.org/wiki/Knights_and_Knaves