# Open problems

> The open frontier of Eternity II in one place: every angle still worth a run, the wall it attacks, what has been tried and where it stopped, and whether it is a newcomer-tractable target or a hard, well-mapped one.

- Canonical page (with interactive figures/demos): https://eternity2.dev/research/open-problems/
- Updated: 2026-07-21
- Source: eternity2 mailing-list archive (groups.io): where the open targets are announced and discussed — https://groups.io/g/eternity2

---
This is the board of open angles: one row per direction still worth a run.
Each entry states the question in a line, names the wall it attacks (from
[why it's hard](/research/why)), points to what has already been tried and
where it stopped (in the [wall-and-method map](/research/why/walls-and-methods)
and the [dead ends](/research/build/dead-ends)), and tags how approachable it
is. The tags mean what they say: **newcomer-friendly** is a target you can pick
up without a decade of context; **hard, well-mapped** is a target that many
strong attempts have charted and none has crossed; **unattended** is an angle
nobody is actively working, distinct from one that has been attacked and held.

For the state of the art the score lives on the [records](/research/records)
page; this page is only the part that is still open.

## The 470-to-480 gap

> **Can any method cross from the 470 ceiling to a full 480?**
>
> The canonical track. The best board respecting only the mandatory starter clue has stood at 470/480 since the community reached it, and a designed 480 is a given: the publisher built the puzzle from one solution, so a perfect board exists and only its location is open.

**Wall.** [Rigidity](/research/why/rigidity-wall): the record boards are
locally frozen islands, and the ten missing edges are on the far side of every
[structural wall at once](/research/why/walls-and-methods).

**Tried, and where it stopped.** Every method in the
[wall-and-method map](/research/why/walls-and-methods) ends against rigidity;
the from-scratch and corpus builds top out at 458 to 463, and none crosses to
the ceiling. Raw compute alone does not close it either, which is recorded
under [just throw more compute at it](/research/build/dead-ends).

**Entry tag.** Hard, well-mapped. This is the summit of the whole puzzle: a
great deal is known about why it resists, which is exactly why a fresh crossing
would be a headline.

## The strict five-clue 464-to-465 target

> **Can a board that honours all five official clues beat 464?**
>
> The strict five-clue line is tracked separately from the open 470 line, because [most progress on the open record was made without the clues](/research/build/clue-puzzles). The best board respecting all five placements is 464.

**Wall.** [Rigidity](/research/why/rigidity-wall) again, plus the clue
placements narrow the reachable region: fewer boards satisfy all five, so the
haystack is smaller but so is the needle count.

**Tried, and where it stopped.** The 464 is the standing strict-line mark on
the [clue puzzles](/research/build/clue-puzzles) page; the project's own strict
builds and re-squeezes reach the 460 class but not past it, as charted in the
[wall-and-method map](/research/why/walls-and-methods).

**Entry tag.** Hard, well-mapped, but a smaller step than the 470-to-480 gap:
464 to 465 is a single edge, on a line where the reachable region is tighter
and therefore easier to reason about than the open record.

## Brendan Owen's hint-free 10x10 set_2

> **Solve set_2, the hint-free 10x10 that has never been solved.**
>
> Brendan Owen published a pair of generated hint-free 10x10 puzzles with their statistics. One (set_1) fell; the other (set_2) has never been solved and remains the community's agreed next rung below the full 16x16.

**Wall.** The same edge-matching hardness as the full puzzle, at a size a
single machine can actually finish. Set_1 took a large but bounded search, so
set_2 is a search-engineering target, not a structural one.

**Tried, and where it stopped.** The full story is on the
[benchmarks](/research/build/benchmarks#brendans-1010s-one-fell-one-is-still-standing)
page: set_1 was solved, set_2's statistics are known, and it is
[still standing](/research/build/benchmarks#brendans-1010s-one-fell-one-is-still-standing).

**Entry tag.** Newcomer-friendly. This is the one open target sized for a
personal machine and a well-tuned backtracker rather than a compute cluster, so
it is the recommended first real attempt.

## Crossing a rigidity basin

> **Is there any local path from one record basin to another?**
>
> Every record board sits in a basin that MIP proofs show is locally optimal out to a multi-cell halo. The open question is whether any sequence of small, legal moves reaches a different basin at all.

**Wall.** [Rigidity](/research/why/rigidity-wall), stated in its sharpest form,
and [why basin-hopping looks impossible](/research/why/sigma-cycles): the step
from one great board to a better one is one giant, indivisible swap with no
gradient to follow.

**Tried, and where it stopped.** The rigidity theorem records MIP proofs of
halo-optimality across several basins, and the search for a short escape chain
between basins failed for a structural reason set out on
[why basin-hopping looks impossible](/research/why/sigma-cycles). The
[recombine two good boards](/research/build/dead-ends) entry is the same wall
from the crossover side.

**Entry tag.** Hard, well-mapped. A single crossing move, or a proof that none
exists, would reshape how every local-search method is judged.

## The meet-in-the-middle memory wall

> **Can the two halves of a meet-in-the-middle search be made to meet at full size?**
>
> Meeting two partial searches in the middle is complete in principle, but the number of partial boards to store grows about twentyfold per extra allowed mismatch, so the halves stop meeting well before the full 16x16.

**Wall.** The exactness cost measured directly: the
[meet-in-the-middle](/research/build/exact/meet-in-the-middle) approach is
exact but its memory grows past what any machine holds.

**Tried, and where it stopped.** BANDSAW solved an endgame band to proven
optimality and in doing so measured the roughly twentyfold-per-mismatch growth
on both sides, so meeting in the middle stops paying at full size; that result
is the [BANDSAW row](/research/why/walls-and-methods) of the map. A better
representation, or a lossy meeting that stays sound, is the open lever.

**Entry tag.** Hard, well-mapped. The wall here is quantified, so progress is
measurable: any encoding that lowers the per-mismatch growth factor is a real
gain even short of a full solve.

## A diversity axis beyond parallel tempering

> **Is there a search mechanism that reliably finds new basins, beyond parallel tempering?**
>
> Almost every method keeps rediscovering the same handful of basins. In a full method sweep, only parallel tempering reliably produced genuinely new ones, and even it plateaus quickly.

**Wall.** [Rigidity](/research/why/rigidity-wall) seen as a diversity
bottleneck: the constraint is not the score a method reaches but the number of
distinct basins it can find, and the standard arsenal finds too few.

**Tried, and where it stopped.** The diversity survey is written up on the
[wall-and-method map](/research/why/walls-and-methods): adaptive local search,
snake placement, and the top of a trained generator's distribution all keep
landing in the known basins, and only parallel tempering reliably escapes.
[Generate boards with a transformer](/research/build/dead-ends) is one of the
diversity attempts that did not hold.

**Entry tag.** Unattended, and open-ended. Unlike the mapped targets above,
this one has no charted attempt list waiting to be beaten: a genuinely new
diversity mechanism is an idea nobody has planted yet, which makes it the most
speculative entry here and the one least constrained by prior work.

## Where these came from, and where to write one up

Every claim above is grounded in a page already on this wiki: the walls in
[why it's hard](/research/why), the stopped attempts in the
[wall-and-method map](/research/why/walls-and-methods) and the
[dead ends](/research/build/dead-ends), the benchmark targets on the
[benchmarks](/research/build/benchmarks) page. If you take one of these on and
it moves, [the notebook is open](/research/contribute) and there is a place for
the write-up.

## Related

- [Records & solvers](https://eternity2.dev/research/records) — Eternity II has never been solved, but fifteen years of community effort have pushed the best board to 470/480. Who holds what, how they did it, and why some headline "480" boards are not actually the real puzzle.
- [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.
- [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.
- [Dead ends](https://eternity2.dev/research/build/dead-ends) — Approaches we tried that look promising and don't move the needle on Eternity II, written down with what we found so you can spend your time elsewhere.
- [The community's benchmarks](https://eternity2.dev/research/build/benchmarks) — How a community forbidden from sharing the pieces built a shared test culture anyway: derived-count verification protocols, the Txibilis and beginner suites, node-count duels, full enumerations, and the one benchmark that is still standing open today.
- [Meet in the middle](https://eternity2.dev/research/build/exact/meet-in-the-middle) — Enumerate two halves of a problem and join them on a shared interface, trading memory for an exponent cut in half. The classic Horowitz–Sahni trick, what it looks like on bands of the board, and what this project's BANDSAW experiment measured, including the one-sided method that beat it.
- [Contribute your research](https://eternity2.dev/research/contribute) — This wiki is the community's research home, and there is room in it for your work. Three ways to get it published, from a mailing-list post to a pull request, plus the small set of house rules that keep every page trustworthy.