Łukasiewicz's single axiom for implicational propositional calculus, $((p\to q)\to r)\to ((r\to p)\to (s\to p))$, is known to be the shortest possible. Does it also have the minimum number of propositional variables, or would it be possible to construct a single, most likely longer, axiom using just 3 propositional variables?
From the answer to this question we get that at least one axiom with 3 variables is needed in order to fully capture implication, so it would be interesting to find out if this minimum can be achieved also with a single axiom.