puzzles

Apples delivery

The distance between the towns A and B is 1000 miles. There is 3000 apples in A, and the apples have to be delivered to B. The available car can take 1000 apples at most. The car driver has developed an addiction to apples: when he has apples aboard he eats 1 apple with each mile made. Figure out the strategy that yields the largest amount of apples to be delivered to B.

Generalize the strategy for an arbitrary amount of apples.

Zen problem

A Buddhist monk got an errand from his teacher: to meditate for exactly 45 minutes. He has no watch; instead he is given two inscent sticks, and he is told that each of those sticks would completely burn in 1 hour. The sticks are not identical, and they burn with variant yet unknown rates (they are hand-made). So he has these two inscent and some matches: can he arrange for exactly 45 minutes of meditation?