Apple Delivery Puzzle

This puzzle describes a constrained transport problem: you have a large stock of identical items in one location, a limited-capacity vehicle, a long distance to a destination, and a rule that items are gradually consumed as the vehicle moves. You are allowed to create temporary depots along the route, shuttling loads back and forth and deciding how far to advance stock at each stage. The question asks for the maximum quantity that can ultimately reach the destination under these rules, turning an apparently simple setup into a nontrivial optimization problem in discrete stages.

Solving it draws on algorithmic thinking about state transitions, piecewise optimization, and reasoning about marginal cost per mile. It rewards candidates who can abstract the situation into phases where the effective "transport cost" changes as the number of remaining loads falls. Interviewers look for an ability to express the loss rate as a function of trips, identify natural breakpoints where strategy should change, and argue about optimality rather than just guessing. A strong answer typically involves clear decomposition, careful accounting, and a structured search over feasible strategies.

What it tests

This problem class is governed by the principle of minimizing cumulative transport losses when moving divisible goods with capacity and per-unit-distance loss constraints. The key is to recognize that when you must make multiple trips to move a large quantity using a limited-capacity vehicle, the cost per mile (in goods lost) is proportional to the number of active loads being moved at each stage. As you progress and the number of remaining goods decreases, you can reduce the number of trips, thus lowering the per-mile loss rate. The optimal solution involves partitioning the journey into segments where the number of trips (and thus the loss rate) drops at natural breakpoints, maximizing the goods delivered to the destination. This structure arises because each additional trip multiplies the loss per mile, so consolidating loads at the right points is crucial for efficiency.