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Combination pipelines

Seven named search experiments that chase score, each a pipeline rather than a single algorithm: it builds a board with one engine, then lifts or finishes it with another. Alongside them, two findings take apart the machinery the pipelines lean on. Each page records its idea, its board, and the questions it left open.

by Raphaël Anjou

pageUpdated 2026-07-22
GAUNTLET

Run the same beam search across nine different scan orders, so it lands in different regions instead of always converging to the same one. The zigzag order found a brand-new 458 board.

CLOISTER

Fix a perfect border, then search the interior with the border's edges treated as hard constraints from the very first cell.

CAS

Place a perfect border ring first, then solve the board inward, shell by shell, each ring as one assignment over the pieces that remain.

MIDDEN

Decide in advance not when a board may break, but where: confine every mismatch to a chosen shape of cells, and search for the best shape.

The fluid frame

A perfect 60-piece border is not one rigid object. Every fully matched frame admits exactly 45 free rim exchanges at zero border cost; a third of perfect frames cannot even start the interior, and a single free exchange revives every one of them.

LADDER

Throw hundreds of cheap short searches at the board, keep only the deepest starts, and promote the survivors through longer and longer rounds.

Making a beam producer 10x better: the answer is width

A verified survey plus paired measurement: no per-node cleverness beats raw beam width at equal wall-clock. The two additives that survive are randomising exactly-tied truncation keys (free) and SMC-style resampling of survivors (small but significant).

MOSAIC

Tile the board into small blocks, solve each one to proven optimality, and glue them together, paying for the seams instead of forbidding them. From scratch, with no record to copy, it reaches 448.

STAGED

Build the whole board from scratch with no pre-set frame, in stages, letting the border emerge last from whatever pieces are left.

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