Codex instance
e27427d231
A selected valley cannot admit a square wider than itself until it reaches the lower neighbouring rim. Reject states whose remaining narrow-square area cannot fill that strip, including width-one and width-two gaps. Keep an unpruned benchmark mode and dedicated counters so the rule remains independently measurable. Record the soundness argument and the measured default-on improvement. Tests: Debug CTest (12 passed) Tests: ASan+UBSan CTest (12 passed) Refs: #10
Partridge
The inspiration for this project is Stand-up Maths' YouTube video The impossible 2025 puzzle with over a million solutions.
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 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
Copyright & Licence
This code is copyright 2025 Matthew Gretton-Dann. Licensed under the Apache-2.0 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.
git clone https://gitea.gretton-dann.org.uk/mgrettondann/partridge-cpp.git
cmake -B build -S partridge-cpp -DCMAKE_BUILD_TYPE=Release
Building
cmake --build build
Executing
N=9 # Set N to largest size of square.
./build/partridge_cpp $N
Testing
See TESTING.md for CTest, Debug, and sanitizer instructions.
Performance measurements use the separate opt-in suite described in BENCHMARKING.md.
The research-only OR-Tools comparison is optional and documented in CP_SAT_REFERENCE.md. It does not affect the native build or its dependencies.