# Partridge

The inspiration for this project is Stand-up Maths' YouTube video 
[The impossible 2025 puzzle with over a million solutions](https://youtu.be/eqyuQZHfNPQ?si=hbOQdVKBC-jwvysk).

In the video Matt Parker shows solutions to the 8th and 9th Partridge
problems, and claims that solutions exist for all Partridge problems from
size eight and above.  (There are no solutions to Partridge problems when N < 8).

Whilst I could see how you can get from a solution to the 2N-th problem to the
(2N+1)th problem I couldn't immediately see that a solution to the 8th & 9th
problems indicate that there would be a solution to the 10th or 12th.

So I set out to write some code that finds a solution to the Partridge problem.

Originally
[I wrote an OCaml version](https://gitea.gretton-dann.org.uk/mgrettondann/partridge-cpp.git)
of the code.  However, my estimate of how long it would take to calculate a
solution to the 10th Partridge problem was around 36 hours on my Macbook Air.
So I moved to C++ which seems to be providing a 3x speed-up just by doing a
straight translation of the code.  There are some further optimisations in the
C++ source which suggest finding a solution to the 10th Partridge problem will take
around 6 hours.

Some results can be seen in [results.md](./results.md)

## Copyright & Licence

This code is copyright 2025 Matthew Gretton-Dann.  Licensed under the
[Apache-2.0 license](./LICENSE).

## Running the code

### Prerequisites

You must have `git`, `cmake`, `make` and a compiler capable of compiling C++20 code
on your path.

### Code checkout and setup.

It is strongly recommended that you make a Release build as shown in the
instructions below.  The code is extremely slow in debug builds.

```sh
git clone https://gitea.gretton-dann.org.uk/mgrettondann/partridge-cpp.git
cmake -B build -S partridge-cpp -DCMAKE_BUILD_TYPE=Release
```

### Building

```sh
cmake --build build
```

### Executing

```sh
N=9 # Set N to largest size of square.
./build/partridge_cpp $N
```