Leap

In EVE Online there is a "early game goal" with the usual rewards for completion. However, the goal is to mine (and another goal to reprocess) some amount of Kernite, an ore that is generally only found in lowsec or more dangerous systems. What to do to complete this goal? One answer is to buy the Kernite off the market, as there is demand in highsec for ore from lowsec. Another solution is to notice that during a particular Career Agent mission (a sort of tutorial series) one must mine some amount of Kernite, which spawns in a high security system. That mission goal only requires a subset of the Kernite available, so someone who has thought about the system might mine out all that Kernite, which happens to be just enough for the early game goal. (The site will despawn when you complete the mission, so you have to mine it out before that.) But there is more! Someone who has really thought about the system may know that asteroid belts respawn at downtime, and thus may wonder whether the mission belt follows the same mechanic as regular asteroid belts, and whether this allows an "infinite"—at least until the game developers change things, or you wander off to do other things—Kernite mine that respawns daily, provided you never complete the career agent mission and thus despawn the Kernite belt. The EVE asteroid belts are more like asparagus, where you 10 lop the tops off 20 wait and 30 GOTO 10.

There is a similar story in "Gödel, Escher, Bach" involving a simple rules system, where if you stay within the rules, you will get nowhere. Only by stepping outside the rules might one notice that the given problem is non-solvable. Oops, spoilers. Also Hamlet dies, etc. Understanding calculus may also require a leap, or leaps.