# Meet in the middle

> Exact endgame experiments that meet in the middle: enumerate a region from two ends and join on the seam, to find the true best completion with a proof rather than a heuristic's best guess. These measure a small region exactly instead of chasing the whole-board score.

- Canonical page (with interactive figures/demos): https://eternity2.dev/research/lab/experiments/raphael-anjou/meet-in-the-middle/
- Updated: 2026-07-17

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Heuristic search guesses; it never knows it has the best possible finish. The
experiments here take the opposite stance for a small region: enumerate it from
two ends, join the halves wherever their seam colours agree and their piece sets
don't overlap, and come away with the *exact* best completion plus a proof that
nothing scores higher. It is the classic
[meet-in-the-middle](/research/build/exact/meet-in-the-middle) time-for-space
trade, pointed at the puzzle's endgame.

These are not attempts on the score. They answer a different question from the
[combination pipelines](/research/lab/experiments/raphael-anjou/pipelines) and the
two search [studies](/research/lab/experiments/raphael-anjou): not *how high can a
heuristic climb*, but *what is the true best ending of this region, and where do
exact methods stop being affordable*. An exact answer about a small region is
worth more here than another near-miss on the whole board.

This is the first experiment of that kind; the section is named for the technique
rather than the one page, because more exact endgame ideas belong alongside it as
they land.

## Pages in this section

- [BANDSAW](https://eternity2.dev/research/lab/experiments/raphael-anjou/meet-in-the-middle/bandsaw) — Solve a band of rows exactly by meeting in the middle, to find the true best ending and to measure how far ahead an endgame can be decided.