It's not O(N^2) is it? It can be a continuous line of ice being pushed up. Depending on the weight bearing ability of the lift and digging capacity, you would figure out a fixed distance after which you would place the buckets to carry up the ice.

Its an interesting interview question at the very least. (More complications arise as and how you get deeper into the ice).

You can't have a continuous line of ice coming up, unless you're digging for slush. Each intact X-meter core must be hauled up on its own, and then the drill has to go back down. The deeper you are, the longer it takes to haul up one core and send the drill back down. So, retrieving the cores is clearly O(N^2).

Drilling the core itself is O(N), but as you go deeper the core retrieval dominates. Not to mention everything getting more complex the deeper you go.

Anyone who has hung a heavy picture/frame? :-)

(you need to pull the drill out periodically to let the dust out, and the distance of that pull increases with depth. But it is O(K1 * N^2 + K2 * N) where K1/K2 are pull-out and drilling-in (both seconds per mm), and for short holes most of the time will be drilling not removing dust.

We need a couple more bore holes to do a Tower of Hanoi style question for interviews.