Balancing subproblems in resilience testing
Drop the first jar at the $\sqrt{n}$th rung, $2\sqrt{n}$th rung, and so on until it breaks at the $m\sqrt{n}$th rung. (This takes at most $\sqrt{n}$ steps). Then drop the second jar at every rung between the $(m-1)\sqrt{n}$th rung and the $m\sqrt{n}$th rung until you find the precise breakpoint.