- Selby–Riordan generator (2007)
- The puzzle was generated to have about one expected solution. Brendan Owen and Günter Stertenbrink derived in 2007 that ~17 interior colors and ~5 border colors put it exactly at the unique-solution boundary — later confirmed as the SAT/CSP phase-transition peak. The hardness is by design.
- Verhaard set-annealing (2008)
- Louis Verhaard's 467 annealed on the composition of piece sets between regions, not just on positions — an early metaheuristic that held the record for over a decade.
- Blackwood heuristic-schedule + break-index (2020)
- The dominant modern algorithm behind every 469/470 board. A scan-row backtracker driven by a piecewise-linear color-exhaustion schedule plus a small set of allowed 'break' depths, run for tens of billions of iterations before restart. Blackwood reported that SAT solvers, GPUs and pre-solved 2×2 caches did not help.
- McGavin's engine (2020–2026)
- A C backtracker hitting ~295 million tile placements per second on one core — roughly 4× a typical community engine — via PGO, aggressive compiler flags and auto-generated per-cell unrolled code. Raw speed plus the right scan order (bottom-left start, left-to-right rows) is half the story of the 469. That headline ~4× is an easy-board figure: on a hard board the same engine runs ~105M, and a portable-Rust reimplementation on this site ties it there (while his C stays ~2.3× faster on easy boards) — though throughput and the score axis are unrelated, and neither engine solves the puzzle.
- Joe's prune-back policy (2026)
- A recent, concrete idea: almost all backtracking time is spent very deep, so if a search spends too long below a depth threshold without progress, prune back to that depth and restart. Measured 17–49% fewer iterations depending on clue count.
The approaches Blackwood and others reported did not help (SAT solvers, GPUs, pre-solved caches) are catalogued in full on the dead ends page.