Matthew Gretton-Dann
1684c289c6
results.md details the results of the Partridge problem for sizes 8, 9 and 10.
60 lines
2.0 KiB
Markdown
60 lines
2.0 KiB
Markdown
# Partridge
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The inspiration for this project is Stand-up Maths' YouTube video
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[The impossible 2025 puzzle with over a million solutions](https://youtu.be/eqyuQZHfNPQ?si=hbOQdVKBC-jwvysk).
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In the video Matt Parker shows solutions to the 8th and 9th Partridge
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problems, and claims that solutions exist for all Partridge problems from
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size eight and above. (There are no solutions to Partridge problems when N < 8).
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Whilst I could see how you can get from a solution to the 2N-th problem to the
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(2N+1)th problem I couldn't immediately see that a solution to the 8th & 9th
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problems indicate that there would be a solution to the 10th or 12th.
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So I set out to write some code that finds a solution to the Partridge problem.
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Originally
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[I wrote an OCaml version](https://gitea.gretton-dann.org.uk/mgrettondann/partridge-cpp.git)
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of the code. However, my estimate of how long it would take to calculate a
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solution to the 10th Partridge problem was around 36 hours on my Macbook Air.
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So I moved to C++ which seems to be providing a 3x speed-up just by doing a
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straight translation of the code. There are some further optimisations in the
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C++ source which suggest finding a solution to the 10th Partridge problem will take
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around 6 hours.
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Some results can be seen in [results.md](./results.md)
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## Copyright & Licence
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This code is copyright 2025 Matthew Gretton-Dann. Licensed under the
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[Apache-2.0 license](./LICENSE).
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## Running the code
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### Prerequisites
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You must have `git`, `cmake`, `make` and a compiler capable of compiling C++20 code
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on your path.
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### Code checkout and setup.
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It is strongly recommended that you make a Release build as shown in the
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instructions below. The code is extremely slow in debug builds.
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```sh
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git clone https://gitea.gretton-dann.org.uk/mgrettondann/partridge-cpp.git
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cmake -B build -S partridge-cpp -DCMAKE_BUILD_TYPE=Release
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```
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### Building
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```sh
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cmake --build build
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```
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### Executing
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```sh
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N=9 # Set N to largest size of square.
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./build/partridge_cpp $N
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``` |