Complete bill set

What this greedy optimization puzzle tests

This is a medium-difficulty combinatorial optimization problem that appears in quant interview loops. It asks you to find the minimal set of items (US dollar bills) that can be combined to form every integer value within a target range. The constraint rewards both mathematical insight and systematic reasoning.

Problems of this type test whether you can balance greedy intuition with exhaustive verification. A natural first instinct—always pick the largest denomination—often fails; the optimal solution requires considering which denominations work together to "cover" gaps. Success hinges on understanding how to represent integers as sums of a small set, and how to verify that no denomination subset has been omitted unnecessarily.

• Greedy algorithms and their failure modes
• Covering problems and completeness verification
• Trade-offs between denomination choices