https://github.com/meithecatte/isabelle-math-contests
Solutions to math olympiad problems in Isabelle/HOL
https://github.com/meithecatte/isabelle-math-contests
Last synced: about 2 months ago
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Solutions to math olympiad problems in Isabelle/HOL
- Host: GitHub
- URL: https://github.com/meithecatte/isabelle-math-contests
- Owner: meithecatte
- Created: 2020-10-05T10:53:07.000Z (over 5 years ago)
- Default Branch: built-pdfs
- Last Pushed: 2021-05-29T22:20:13.000Z (over 4 years ago)
- Last Synced: 2025-01-30T19:49:15.773Z (about 1 year ago)
- Size: 6.94 MB
- Stars: 11
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Isabelle/HOL solutions to math contest problems
This repository contains various [Isabelle/HOL] formal proofs. This is mostly solutions
to interesting math olympiad problems, but some higher math exercises have found their way
here, too.
Apart from that, I keep some [notes] on the mathematical library of Isabelle. This includes
situations where the structure and interaction of objects
I encourage you to explore.
[notes]: https://github.com/NieDzejkob/isabelle-math-contests/blob/master/NOTES.md
[Isabelle/HOL]: https://isabelle.in.tum.de/
## Problems by tag
-
number theory [8 problems]
- [BMO1 2015 Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/BMO1/2015/BMO1-2015-Problem_2.pdf) (number theory)
- [Canada MO 2020 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Canada_MO/2020/Canada_MO-2020-Problem_1.pdf) (number theory)
- [Greece MO 2007 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Greece_MO/2007/Greece_MO-2007-Problem_1.pdf) (number theory)
- [Polish MO 1969 Round 1 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_1.pdf) (number theory, diophantine equation)
- [Polish MO 1969 Round 1 Warmup Problem A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_A.pdf) (number theory, congruences)
- [Polish MO 2020 Round 1 Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_3.pdf) (number theory)
- [Polish MO 2020 Round 2 Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_3.pdf) (number theory)
- [USAMO 2006 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)
-
combinatorics [4 problems]
- [APMO 2013 Problem 4](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/APMO/2013/APMO-2013-Problem_4.pdf) (combinatorics)
- [IMO 2019 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_5.pdf) (combinatorics)
- [Polish MO 2020 Round 2 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_1.pdf) (combinatorics)
- [USAMO 2006 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)
-
functional equation [3 problems]
- [Deltami 44M Problem 789](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Deltami_44M/Deltami_44M-Problem_789.pdf) (functional equation)
- [IMO 2019 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_1.pdf) (functional equation)
- [Unknown Origin Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Unknown_Origin/Unknown_Origin-Problem_1.pdf) (functional equation)
-
real analysis [3 problems]
- [IMC PoTD 15](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMC/IMC-PoTD_15.pdf) (real analysis)
- [Polish MO 1969 Round 1 Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_2.pdf) (real analysis)
- [Polish MO 1969 Round 1 Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)
-
inequality [3 problems]
- [Polish MO 1969 Round 1 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_5.pdf) (inequality)
- [Polish MO 1969 Round 1 Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)
- [Polish MO 2020 Round 1 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_1.pdf) (inequality)
-
group theory [2 problems]
- [Napkin Problem 1A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1A.pdf) (group theory)
- [Napkin Problem 1B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1B.pdf) (group theory)
-
diophantine equation [1 problem]
- [Polish MO 1969 Round 1 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_1.pdf) (number theory, diophantine equation)
-
congruences [1 problem]
- [Polish MO 1969 Round 1 Warmup Problem A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_A.pdf) (number theory, congruences)
-
multiple solutions [1 problem]
- [Polish MO 1969 Round 1 Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)
-
equation over reals [1 problem]
- [Polish MO 1969 Round 1 Warmup Problem C](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_C.pdf) (equation over reals)
-
metric space [1 problem]
- [Polish MO 1969 Round 1 Warmup Problem D](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_D.pdf) (metric space, geometry)
-
geometry [1 problem]
- [Polish MO 1969 Round 1 Warmup Problem D](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_D.pdf) (metric space, geometry)
-
nondeterministic process [1 problem]
- [USAMO 2006 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)
## Problems by origin
-
Asia Pacific Math Olympiad [1 problem]
- 2013
- [Problem 4](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/APMO/2013/APMO-2013-Problem_4.pdf) (combinatorics)
-
British Maths Olympiad Round 1 [1 problem]
- 2015
- [Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/BMO1/2015/BMO1-2015-Problem_2.pdf) (number theory)
-
Canada Math Olympiad [1 problem]
- 2020
- [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Canada_MO/2020/Canada_MO-2020-Problem_1.pdf) (number theory)
-
Deltami 44M [1 problem]
- [Problem 789](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Deltami_44M/Deltami_44M-Problem_789.pdf) (functional equation)
-
Greece Math Olympiad [1 problem]
- 2007
- [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Greece_MO/2007/Greece_MO-2007-Problem_1.pdf) (number theory)
-
Instagram Math Community [1 problem]
- [PoTD 15](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMC/IMC-PoTD_15.pdf) (real analysis)
-
International Math Olympiad [2 problems]
- 2019
- [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_1.pdf) (functional equation)
- [Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_5.pdf) (combinatorics)
-
An Infinitely Large Napkin [2 problems]
- [Problem 1A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1A.pdf) (group theory)
- [Problem 1B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1B.pdf) (group theory)
-
Polish Math Olympiad [11 problems]
- 1969
- Round 1
- [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_1.pdf) (number theory, diophantine equation)
- [Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_2.pdf) (real analysis)
- [Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_5.pdf) (inequality)
- [Warmup Problem A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_A.pdf) (number theory, congruences)
- [Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)
- [Warmup Problem C](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_C.pdf) (equation over reals)
- [Warmup Problem D](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_D.pdf) (metric space, geometry)
- 2020
- Round 1
- [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_1.pdf) (inequality)
- [Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_3.pdf) (number theory)
- Round 2
- [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_1.pdf) (combinatorics)
- [Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_3.pdf) (number theory)
-
United States of America Math Olympiad [1 problem]
- 2006
- [Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)
-
Unknown Origin [1 problem]
- [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Unknown_Origin/Unknown_Origin-Problem_1.pdf) (functional equation)
## Structure of this repository
Raw Isabelle `.thy` files are hard to look at. As can be expected for math,
lots of non-ASCII characters are involved. Apart from font issues, Isabelle actually
predates Unicode, so the text files are actually encoded with LaTeX-ish escape sequences.
This motivates a sophisticated CI setup (the three words you don't ever want to see next
to each other). The `master` branch of the repository keeps the sources, while GitHub
Actions render PDFs and push them onto the `built-pdfs` branch.