Cash Denomination Planner

How to use Cash Denomination Planner

A bounded dynamic program minimizes item count for each amount. Monotone queues consider each denomination’s allowed stock, and recorded stage choices reconstruct a feasible optimum. Greedy selection is not assumed correct.

1. Enter amount in whole minor units, allowed whole-unit denominations, optional matching stock counts; blank means unlimited.
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• Whole minor-unit amount0–100000,1–30 unique positive denominations up to100000, optional matching whole stock limits0–100000. At most3million amount-stage positions; no live currency or legal-tender assumptions.
• Runs locally. Text/JSON fields are capped at30,000 characters; stricter page-specific and numeric-string limits also apply. Numeric inputs are bounded to magnitude1e15 and nonzero magnitude at least1e-100 unless an exact-string mode states otherwise. Approximate summaries use12 significant digits; CSV numeric cells retain the complete stored value and potentially formula-like string cells gain a protective apostrophe; unsupported, non-finite or detected underflow states return an error.
• Educational user-assumption arithmetic only. No live prices, laws, tax rules, quotes or financial advice.