Evil 25×25 Picross — Nested Hypothesis Chains Across 625 Cells

Evil 25×25 Picross is a week-long analytical project for most solvers. Primary hypothesis chains run twenty-four to thirty-six steps before resolving, many configurations require Level 2 hypotheses embedded within the primary chain's conditional world — with Level 2 chains themselves running fourteen to twenty-two steps — and twenty-two to thirty-four primary cycles are required to resolve the full 625-cell grid. The total session time ranges from fifteen to thirty hours across ten or more sessions spread over several days.

What "Evil" Means at 25×25

Evil 25×25 combines the properties of 25×25 Extreme with the nested hypothesis structure that first appears at smaller Evil sizes, at a scale that magnifies every component significantly.

Extended primary chains: Twenty-four to thirty-six steps — the longest primary chains at any Evil size below 30×30. Each step in a 50-line grid can update twenty-five perpendicular constraint states simultaneously, and the sub-deductions that cascade within each step add further intermediate documentation requirements.

Nested Level 2 hypotheses: When the primary chain reaches an ambiguous intermediate state, a Level 2 hypothesis is opened within the primary chain's conditional world. At 25×25, Level 2 chains run fourteen to twenty-two steps — longer than the complete hypothesis cycles at Expert 12×12 or Expert 15×15. Level 2 requires the same documentation thoroughness as Level 1, applied to a constraint state that is itself conditioned on Level 1's intermediate assumptions.

High cycle count with cascade suppression: Twenty-two to thirty-four primary cycles, each with two to five further direct deductions post-confirmation, accumulates a total documentation record across a complete solve that can approach three thousand documented steps. At this volume, documentation architecture is not a convenience — it is the infrastructure that makes the solve tractable at all.

The Evil 25×25 Solving Approach

Standard exhaustion: Apply all methods fully — 120–180 minutes in a single dedicated session. Document the resulting grid state as Session 1 output.

Documentation architecture: Three primary documents as at 25×25 Extreme (grid state, cycle log, arrangement record), plus a fourth: a hypothesis-level tracking document that records, for each primary cycle, the Level 1 chain steps and any Level 2 branches with their entry points, resolutions, and the Level 1 continuation steps that followed. This fourth document is the key addition for Evil versus Extreme — it provides the complete record needed to verify that Level 2 unwinds were executed correctly relative to the Level 1 chain's continuation.

Primary cycle execution: Assume the first valid arrangement for the selected line. Execute the Level 1 chain with full step documentation. When Level 2 is required, open it clearly in the hypothesis-level tracking document. Execute Level 2 fully, resolving it to contradiction or confirmation. Record the Level 2 resolution, the effect on Level 1 continuation, and any Level 2 marks that were unwound. Continue the Level 1 chain. Find the Level 1 contradiction or confirmation. Execute the Level 1 unwind or confirmation precisely.

Session protocol: Complete each session at a clean cycle boundary — after the post-cycle standard pass is complete and the arrangement record has been updated for the next cycle's hypothesis target selection. Never pause within an active Level 1 or Level 2 chain. At each session start, execute the three-point state verification (grid state, cycle log, arrangement record) plus a review of the hypothesis-level tracking document to confirm that the last session ended at a clean boundary.

Error recovery at scale: If the grid reaches a contradictory state — cells that must simultaneously be filled and empty — the error most likely originated two to five primary cycles earlier. At 25×25, tracing back through five cycles of documented steps to find the source is a significant effort. The most reliable recovery approach: identify the most recent session boundary at which the grid state was explicitly verified as consistent, restore the grid to that state using the session output documentation, and re-execute from that session start. This approach requires sacrificing one session's work but is consistently faster than attempting to trace the error forward through five cycles of documentation.

Evil 25×25 and the Progression to 30×30

Evil 25×25 directly prepares solvers for 30×30 Evil — the platform maximum. The same two-level documentation architecture, session protocol, and error recovery approach apply at 30×30, with longer chains, more lines, higher cycle counts, and correspondingly greater session commitments. Completing Evil 25×25 establishes every habit and system that 30×30 Evil requires at still greater scale.

→ 30×30 Evil — the platform maximum: 900 cells, 60 lines, nested hypothesis chains

→ 20×20 Evil — the same nested technique with a 40-line network and shorter chains

→ 25×25 Extreme — if Evil feels premature, Extreme builds the multi-day multi-session discipline Evil extends with nested hypothesis structure

Stuck? At Evil, the 25×25 Solver is most useful as a session-start validation tool — comparing the solver's constraint state assessment at the start of each session against the documented state in the grid state file.