# Where the mismatches live > A near-perfect board doesn't scatter its few errors evenly. It packs them into one band of five rows and leaves all the rest flawless. Which band is decided by the direction the search filled the board, and you can see the mirror on the real record boards. - Canonical page (with interactive figures/demos): https://eternity2.dev/research/why/mismatch-geometry/ - Updated: 2026-07-02 - Topics: structure - Source: Peter McGavin's 469-record announcement: the board whose eleven unmatched edges this page analyses (groups.io msg 10045, September 2020) — https://groups.io/g/eternity2/message/10045 --- Score a record board edge by edge and a striking thing shows up: the mismatches are not spread around. McGavin's 469 has all eleven of its unmatched edges in the top five rows (rows 0 to 4); rows 5 through 15 are locally perfect. The board is, in effect, a flawless 11-row slab with all the damage swept up against one edge. Now score this project's best from-scratch boards the same way. The damage is again in a five-row band, but at the bottom. KEYRING's and GAUNTLET's mismatches sit in rows 11 to 15, with rows 0 through 10 perfect. It is the same picture flipped top to bottom. ## See it on the real boards Pick a board. The shaded band is where its mismatches actually fall, computed live with the engine's own scoring rule: community boards at the top, this project's at the bottom. > **[Figure]** Interactive: where mismatches are forced to live — interactive: MismatchGeometryLab. Rendered on the canonical page (link above); not shown in this markdown export. ## Why it flips: scan order The flip is not a coincidence; it is the fingerprint of how each board was built. A search that fills the board from the bottom up spends its perfect placements early, low down, and is forced to absorb every accumulated conflict in the last rows it reaches: the top. A search that fills top-down does the exact opposite and piles the damage at the bottom. The mismatches always end up crammed against the edge the solver finished at. Same puzzle, same kind of board, opposite construction order. ## The same band, under a different objective The pattern is not an artefact of how we score. Some solvers optimise a different thing entirely: not matched edges on a full board, but the most pieces you can place with zero conflicts, leaving holes instead of mismatches. Run that objective and the holes land in the same place. Louis Verhaard's "Only seven holes" board places 249 of 256 pieces conflict-free, and all seven holes sit in rows 1 to 4, the top band again. Laurent Zamofing, reaching a similar ceiling in 2026 by recombining the community's record boards, noted the same thing: "the unsolved residual always lands in that top band" ([msg 11901](https://groups.io/g/eternity2/message/11901)). Two objectives that share nothing but the puzzle, and the leftover damage collects against the same edge. It is the construction order, not the scoring rule, that decides where the difficulty ends up. (More on this variant on the [variants page](/research/build/variants).) ## What it tells us This is the visible form of two deeper facts. First, the great boards really are almost-complete: the gap to 480 is concentrated, not diffuse, which is why integer programming finds them locally frozen everywhere except that one band (the rigidity wall). Second, it says the endgame is the whole game: whichever rows you fill last are where the puzzle makes you pay, so the order you search in decides where the difficulty lands. That is the same lesson the playground's path-racing makes you feel, here written into the structure of every record board. > **Note** > > The per-row counts and the highlighted band are computed in your browser from the real board edges (the same scoring rule the engine uses), not hand-placed. The underlying finding and the scan-order explanation are recorded in the project lab notebook. ## Related - [The rigidity wall](https://eternity2.dev/research/why/rigidity-wall) — Every record board we have is frozen in place. You cannot nudge your way from a great board to a perfect one, and we can prove it. - [STAGED](https://eternity2.dev/research/lab/experiments/raphael-anjou/pipelines/staged) — Build the whole board from scratch with no pre-set frame, in stages, letting the border emerge last from whatever pieces are left. - [Which wall stops which method](https://eternity2.dev/research/why/walls-and-methods) — The research section has two halves: the structural walls that make Eternity II hard, and the algorithms built to climb them. This page is the bridge: each method lined up against the wall it actually attacks, and the score where that wall stopped it. - [Why basin-hopping looks impossible](https://eternity2.dev/research/why/sigma-cycles) — If you can't improve a great board by polishing it, maybe you can jump to a different great board. On every record pair tested, you can't, and the structural reason why is worth seeing.