The concept of reachability is pretty interesting in general as well.<p>"Can a spaceship with a certain delta-v reach another planet within an n-body system? (And if so, what is the fastest-to target/most resource preserving acceleration schedule?)" - apparently necessitates brute force, practically not computable on long time scales due to the chaos inherent in n-body systems (<a href="https://space.stackexchange.com/questions/64392/escaping-earth-how-could-one-attempt-to-find-the-best-solution-to-this-traject" rel="nofollow noreferrer">https://space.stackexchange.com/questions/64392/escaping-ear...</a>, <a href="https://en.wikipedia.org/wiki/N-body_problem" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/N-body_problem</a>)<p>"Can a math proof be reached (within a certain number of proof steps) from the axioms?" - equivalent to the halting problem in most practical systems (<a href="https://math.stackexchange.com/questions/3477810/estimating-meta-mathematical-properties-of-conjectures" rel="nofollow noreferrer">https://math.stackexchange.com/questions/3477810/estimating-...</a>)<p>"Can a demoscene program with a very limited program size visualize (or codegolf program output) something specific?" - asking for nontrivial properties like this usually requires actually running each program, and there are unfathomably many short programs (<a href="https://www.dwitter.net/" rel="nofollow noreferrer">https://www.dwitter.net/</a> is a good example of this)<p>"In cookie-clicker games, is it possible to go above a certain score within a certain number of game ticks using some sequence of actions?" - in all but the simplest and shortest games (like <a href="https://qewasd.com" rel="nofollow noreferrer">https://qewasd.com</a>), this is at least not <i>efficiently</i> (optimally) solvable using MILP and the like, as the number of possible action sequences increases exponentially<p>And yet, despite these being really hard (or in the general case, impossible) problems, humans use some heuristics to achieve progress