Reproduceseeded — reproduces with the given seed·reruns the search (See below)·Budget: ~30 s × 8 seeds (exploratory run, not the standardized single-core bench)
Pipeline
1
frame input
A pre-solved 60-piece perfect border is fixed as the starting frame
2
break DFS
Break-tolerant DFS fills the 14×14 interior, pruning doomed lines against the frame from cell one
3
exact tail
A 14-cell exact endgame seals the interior against the rim deterministically
Complexity
Time
per frame: ~6 s hint-compatibility probe, then a 30 s tail recipe × 8 seeds
Space
one DFS frontier over the 14×14 interior; the 60-piece frame is fixed
Fixing the border collapses the joint border-interior search to an interior- only one, which is what makes the exact endgame tractable.
Hardware & run
Native runCPU only
0.067core-hours
Cores
8
RAM
16 GiB
GPUs
0
CPU
Apple M1
Machine
MacBook (Apple M1, 8 cores)
Budget
~30 s × 8 seeds (exploratory run, not the standardized single-core bench)
The border and the interior are usually solved together, which wastes effort:
the interior keeps proposing pieces that can't possibly meet the border
later. CLOISTER pins a perfect 60-piece frame first, then searches the 14×14
interior with the frame's inward-facing edges as real constraints from cell
one, so a doomed interior is rejected immediately instead of at the end.
Start from a complete, perfectly-matched border. The interior search is a
break-allowing depth-first fill, but the cells along the inner edge of the
frame must match the frame, and that requirement is live from the first
placement, not checked only when the interior is finished. Exact endgames
score the last region, including how well it seals against the rim.
Because the border is fixed, the search collects something a post-hoc
interior can't: the handful of extra edges that come from the interior
actually fitting the rim it was built against, rather than being grafted onto
a rim later.
▶Interactive: how the frame anchors the interiorExplore →
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Try it live: fix a frame and watch the interior search run against it in your
browser.
▶Interactive: solve the standalone interior liveExplore →
As a standalone interior solver CLOISTER reaches an interior score of 453
unhinted, in minutes, and confirms a real effect: an interior built against
its own rim attaches with a few more matched edges than the same-quality
interior attached after the fact. With all five official clues forced it
settles in the high 440s to low 450s.
It doesn't break the top records, and it saturates like everything else does
near the wall. But it cleanly isolates and measures the border-interior
coupling that whole-board search blurs together.
The search is a break-tolerant DFS over the interior, but the leverage is in
the framing and a two-phase campaign over many frames.
Frame as hard constraint. A complete 60-piece border is fixed, and the
frame's inward-facing colours become hard constraints on the rim cells from
the very first interior placement, not a check deferred to the end. A doomed
interior is pruned immediately.
Exact tail. The endgame region is solved exactly (a 14-cell exact tail),
including how it seals against the rim, so the last few cells are closed
deterministically rather than by heuristic.
Frame-breadth campaign. Rather than one border, sweep a directory of
candidate frames in two phases: a cheap ~6-second hint-compatibility probe
drops frames that can't host the clues, then a 30-second tail recipe runs
over each surviving frame with 8 seeds. The best interior wins.
The measured effect is small but real, and it comes from one thing: the
border-interior coupling that whole-board search averages away, but that a
rim-first build gets to exploit while it still can. 453 unhinted; high-440s to
low-450s with all five clues forced.
Seeded and close to deterministic given a frame: the DFS interior solve off a
fixed frame reproduces its score reliably, and the committed board is checkable
edge by edge in the viewer. The solve needs one input beyond the puzzle, a
pre-solved perfect border frame; a runnable backing directory that ships that
frame alongside the engine is planned.
How much of the rim-compatibility bonus can be collected without fixing the
border first? Does scanning many borders, rather than one, find an interior
that attaches better still? And where exactly does the strict-clue version's
ceiling come from?