Solved at Scale

Honest Solver Scope

Propagation is still exact and still the right first move; the solver's contribution is committing to one real schedule when propagation cannot narrow the space. The chapter's claims stop at one pinned instance, with no runtime or scaling promises.

highlighted = computed this step

Propagation is still exact

Nothing here replaces the earlier chapters: propagation is still sound and still the right first move — prune what is forced. Why: propagation never removes a feasible value; on this instance it is not wrong, just insufficient alone, because the feasible space stays large.

prune what is forced first\text{prune what is forced first}
Propagation first, search when stuckThe solver's schedule for the pinned instance; propagation alone cannot pick it.one committed schedule of 5184D1D2D3N1S3S2off2 shiftsN2S2S1S23 shiftsN3offS3S12 shiftsN4S1offS32 shifts

Search commits

The solver's contribution is search that commits to one actual schedule when propagation cannot narrow further: branch when stuck, then prune again under the new assumption. Why: the stuck toy showed the pattern on three variables; the same loop delivers a concrete feasible schedule on the real instance.

propagate→branch→propagate\text{propagate}\rightarrow\text{branch}\rightarrow\text{propagate}
Propagation first, search when stuckThe solver's schedule for the pinned instance; propagation alone cannot pick it.one committed schedule of 5184D1D2D3N1S3S2off2 shiftsN2S2S1S23 shiftsN3offS3S12 shiftsN4S1offS32 shifts

Transfer boundary

The honest boundary: this chapter certifies one pinned 4 by 3 by 3 instance — one decoded schedule re-verified against 25 constraints and one enumeration count — and says nothing about solver runtimes or larger instances. Why: feasibility on a small instance is exact knowledge about that instance, not a performance promise about a different one. Pixel positions are rounded for layout; every number shown is exact.

exact here; no runtime promise elsewhere\text{exact here; no runtime promise elsewhere}
Propagation first, search when stuckThe solver's schedule for the pinned instance; propagation alone cannot pick it.one committed schedule of 5184D1D2D3N1S3S2off2 shiftsN2S2S1S23 shiftsN3offS3S12 shiftsN4S1offS32 shifts