Files

T

Codex instance 0a7ce1e49e bench: add optional CP-SAT reference

Provide a separately installed OR-Tools model to compare a generic constraint solver with the native first-solution path without adding a production or default-test dependency.

Use no-overlap, exact-fill, edge and equal-copy symmetry constraints, validate placements independently, and record model size, memory, worker count and timings for orders 8 and 9. Keep the tool only as a reference and defer DLX absent new evidence.

Tests: Release CTest (9 passed)

Tests: Python reference tests and compilation checks

Tests: independently validated CP-SAT orders 8 and 9

Refs: #5

2026-07-30 17:40:17 +01:00

2.3 KiB

Raw Blame History

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

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.

2.3 KiB Raw Blame History