Evil 15×15 Picross — Nested Hypothesis Chains Across 225 Cells

Evil 15×15 Picross is a 3–5 hour analytical undertaking. Clue density is maximised, primary hypothesis chains run sixteen to twenty-four steps before resolving, some configurations require a nested secondary hypothesis within the primary chain's conditional world, and the 30-line constraint network means every step and every unwind involves more perpendicular state updates than at any smaller Evil size. This is a multi-session format for most solvers — and one of the most demanding Picross experiences available anywhere.

What "Evil" Means at 15×15

Evil 15×15 configurations combine three compounding properties at a grid scale that amplifies the demand of each.

Extended primary chains: Primary cycles run sixteen to twenty-four steps — longer than at any smaller Evil size — because the 30-line network produces more intermediate deductions between steps and the high-slack clue configurations extend the time before a contradiction becomes visible.

Nested secondary hypotheses: Some Evil 15×15 configurations require a secondary hypothesis embedded within the primary chain. The Level 2 assumption operates within the constraint state that Level 1 has established, resolves to contradiction or confirmation, and its result is used to continue the Level 1 chain. At 15×15, Level 2 chains themselves can run eight to twelve steps before resolving — a length that requires Level 2 documentation as thorough as a full Expert cycle at 10×10.

Cascade suppression with high cycle count: Post-cycle cascades generate two to five direct deductions, maintaining a high total cycle count (typically fourteen to twenty-two complete primary cycles). Combined with the longer individual chains, this produces a total analytical load substantially greater than at 12×12 Evil.

The Evil 15×15 Solving Approach

Standard exhaustion: Apply all methods fully. At 15×15 Evil, the standard phase typically resolves 150–175 cells. Document the resulting grid state precisely — this baseline is referenced repeatedly across the multi-session solve.

Two-level documentation: Maintain separate documentation for Level 1 and Level 2 hypothesis deductions. A three-column format works well at 15×15: column 1 records the hypothesis level (L1 or L2), column 2 records the deduction (cell, fill or empty, source), column 3 records the constraint-state changes in affected perpendicular lines. The third column is the critical addition at 15×15 — tracking arrangement count changes as the chain progresses allows correct hypothesis target selection for any embedded Level 2 without re-deriving the conditional constraint state from scratch.

Level management: When Level 2 resolves by contradiction, unwind all Level 2 marks and continue the Level 1 chain with the confirmed cell. When Level 1 resolves by contradiction, unwind all Level 2 marks first (if any remain), then all Level 1 marks, then confirm the opposite of the primary assumption and re-run the post-cycle standard pass.

Session planning: Evil 15×15 is not a single-sitting puzzle for most solvers. A three-session structure works well: Session 1 — standard exhaustion phase; Session 2 — hypothesis cycles 1 through 8 approximately; Session 3 — remaining cycles to completion. At each session boundary, document the complete grid state, all arrangement notations for unresolved lines, and the complete Level 1 and Level 2 documentation from any cycle that was open at the boundary. Resume only from a clean cycle start — never stop in the middle of an active hypothesis chain.

Evil 15×15 and the Larger Grid Progression

The nested hypothesis framework used at 15×15 Evil carries directly to 20×20 Evil and beyond — the same two-level structure, the same documentation requirements, the same cycle management discipline. At 20×20 and above, chains are longer, cycle counts are higher, and session commitments extend to six or more hours. Evil 15×15 is the most demanding format at which the complete methodology can be established before the additional scale of larger grids is introduced.

→ 20×20 Evil — nested hypothesis chains across a 40-line, 400-cell grid

→ 12×12 Evil — the same nested technique with shorter chains and a 24-line network

→ 15×15 Extreme — if Evil feels premature, Extreme builds the multi-cycle and documentation discipline Evil requires at this grid size

Stuck? At Evil, the 15×15 Solver is most useful as a session-boundary validation tool — comparing the solver's constraint state assessment at each session start against your documented state identifies any documentation drift before it propagates into the next cycle block.