Expensive fuel

What this optimization puzzle tests

This is a hard puzzle that combines discrete optimization with resource allocation under a budget constraint. It requires you to think strategically about when and where to purchase fuel as the cost structure changes, and to recognize patterns that allow you to scale a solution efficiently.

The problem forces you to balance competing objectives: minimizing wasted spending versus maximizing distance. Since traders are positioned at quadratic intervals and fuel costs scale linearly per unit, the structure rewards careful planning rather than greedy local choices. You'll need to set up equations or recursive relationships that capture the trade-off between buying fuel early (cheaper per unit) and buying it later (closer to your destination).

• Quadratic spacing and cumulative distance calculations
• Cost structure and marginal pricing
• Dynamic programming or greedy algorithm design
• Constraint satisfaction under a fixed budget