https://github.com/uncomputable/expressive-wallet

What is a minimal wallet of coins that can express all amounts below a target?
https://github.com/uncomputable/expressive-wallet

coq formal-verification maths maths-problem ocaml theorem-proving

Last synced: 11 days ago
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What is a minimal wallet of coins that can express all amounts below a target?

• Host: GitHub
• URL: https://github.com/uncomputable/expressive-wallet
• Owner: uncomputable
• License: cc0-1.0
• Created: 2023-11-12T21:50:36.000Z (about 1 year ago)
• Default Branch: master
• Last Pushed: 2023-11-18T16:00:59.000Z (about 1 year ago)
• Last Synced: 2024-11-06T05:43:20.731Z (about 2 months ago)
• Topics: coq, formal-verification, maths, maths-problem, ocaml, theorem-proving
• Language: Coq
• Homepage:
• Size: 30.3 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Expressive Wallet Problem

Trigger warning: math ⚠️

"Given a set of coin denominations, what is a minimal wallet that can express all amounts up to a target amount?"

This math problem actually has some use in daily life! Always pay the bill exactly ✅

## Example: Euro cents 1, 2, 5, 10, 20, 50

Here are minimal wallets for targets 0 to 100.

It is surprising how slowly the wallet grows with respect to the target. I can't help but see a skyscraper.

| Target | Minimal Wallet               |

|--------|------------------------------|

| 0      | []                           |

| 1      | [1]                          |

| 2      | [1, 2]                       |

| 3      | [1, 2]                       |

| 4      | [1, 2, 2]                    |

| 5      | [1, 2, 2]                    |

| 6      | [1, 2, 2, 5]                 |

| 7      | [1, 2, 2, 5]                 |

| 8      | [1, 2, 2, 5]                 |

| 9      | [1, 2, 2, 5]                 |

| 10     | [1, 2, 2, 5]                 |

| 11     | [1, 2, 2, 5, 10]             |

| 12     | [1, 2, 2, 5, 10]             |

| 13     | [1, 2, 2, 5, 10]             |

| 14     | [1, 2, 2, 5, 10]             |

| 15     | [1, 2, 2, 5, 10]             |

| 16     | [1, 2, 2, 5, 10]             |

| 17     | [1, 2, 2, 5, 10]             |

| 18     | [1, 2, 2, 5, 10]             |

| 19     | [1, 2, 2, 5, 10]             |

| 20     | [1, 2, 2, 5, 10]             |

| 21     | [1, 2, 2, 5, 10, 20]         |

| 22     | [1, 2, 2, 5, 10, 20]         |

| 23     | [1, 2, 2, 5, 10, 20]         |

| 24     | [1, 2, 2, 5, 10, 20]         |

| 25     | [1, 2, 2, 5, 10, 20]         |

| 26     | [1, 2, 2, 5, 10, 20]         |

| 27     | [1, 2, 2, 5, 10, 20]         |

| 28     | [1, 2, 2, 5, 10, 20]         |

| 29     | [1, 2, 2, 5, 10, 20]         |

| 30     | [1, 2, 2, 5, 10, 20]         |

| 31     | [1, 2, 2, 5, 10, 20]         |

| 32     | [1, 2, 2, 5, 10, 20]         |

| 33     | [1, 2, 2, 5, 10, 20]         |

| 34     | [1, 2, 2, 5, 10, 20]         |

| 35     | [1, 2, 2, 5, 10, 20]         |

| 36     | [1, 2, 2, 5, 10, 20]         |

| 37     | [1, 2, 2, 5, 10, 20]         |

| 38     | [1, 2, 2, 5, 10, 20]         |

| 39     | [1, 2, 2, 5, 10, 20]         |

| 40     | [1, 2, 2, 5, 10, 20]         |

| 41     | [1, 2, 2, 5, 10, 20, 20]     |

| ...    | ...                          |

| 60     | [1, 2, 2, 5, 10, 20, 20]     |

| 61     | [1, 2, 2, 5, 10, 20, 20, 50] |

| ...    | ...                          |

| 100    | [1, 2, 2, 5, 10, 20, 20, 50] |