Medium 15×15 Picross — Sustained Cross-Referencing Across 30 Lines

Medium 15×15 Picross is a 35–60 minute analytical session across 225 cells. The 30-line constraint network, multi-block clues with meaningful slack, and the cascading cross-referencing passes that build constraint data progressively across a large grid — this is the difficulty level that defines what large-format Picross feels like as a solving experience.

What "Medium" Means at 15×15

The first overlap pass on a Medium 15×15 resolves approximately 60–90 cells — roughly 30–40% of the grid. The remaining 135–165 cells come from sustained multi-pass cross-referencing: cycles in which each confirmed cell propagates constraint data into its perpendicular line, reduces that line's valid arrangement count, and enables further confirmations in the next pass.

At 15×15, the "7" clue presents the key challenge that the "6" clue introduced at 12×12 and the "5" clue at 10×10: a single-block clue with slack equal to its block length, producing zero direct overlap and complete dependence on imported perpendicular data. At 15 cells, any single-block clue of "7" or shorter falls into this category — a larger proportion of clue sizes than at any smaller grid. Medium 15×15 configurations include several such lines, and managing them through progressive cross-referencing over multiple passes is the core discipline the format builds.

The Medium 15×15 Solving Approach

Step 1 — Overlap pass: Process all 30 lines. Mark every direct result. Note which lines produced zero confirmed cells and which produced partial results — this distinction matters for prioritising which lines to revisit first in the cross-reference phase.

Step 2 — Prioritised propagation: After each confirmed cell, update the perpendicular line's constraint state immediately. On a 30-line grid, immediate propagation is even more valuable than at smaller sizes — deferring column updates to the end of the row-pass means the first 14 rows don't benefit from column constraint data established during the pass itself. Propagating immediately after each confirmation treats every confirmed cell as a seed for the next deduction rather than a deferred batch.

Step 3 — Progressive line revisits: After each full pass cycle, return to the lines that produced no results in the previous passes. Process them in order of most likely to have benefited from perpendicular fills — lines whose perpendicular lines produced many confirmed cells in the previous pass should be checked first.

Step 4 — Repeat: Medium 15×15 requires six to ten full pass cycles before the grid resolves. No enumeration, no hypothesis — overlap analysis and disciplined cross-referencing is sufficient throughout.

Tracking Progress Across 30 Lines

At 30 lines, losing track of which lines have been updated since the last pass is the most common source of artificial dead ends at Medium difficulty. A two-status notation works well: mark each line as either "processed this pass" or "not yet processed." Clear all marks at the end of each pass before starting the next. This practice makes every stuck-feeling moment immediately diagnosable — either a line was skipped (check the notation) or the grid genuinely needs more perpendicular data (continue to the next pass).

Ready to Progress?

→ 15×15 Hard — arrangement enumeration becomes necessary across the 225-cell grid

→ 15×15 Easy — if Medium feels too large a step, Easy builds the systematic pass discipline Medium requires

→ 20×20 Medium — the same cross-referencing challenge at the next large-format scale

Stuck? The 15×15 Solver identifies your next step.