Medium 15×15 Nonograms — 30-Line Logic Across a 225-Cell Grid

Medium 15×15 nonograms are the first format where the full experience of large-scale nonogram solving becomes apparent. The 225-cell grid and 30-line constraint network, combined with Medium difficulty clue density, create puzzles that require genuine multi-session engagement at the upper end — and deliver cascade effects of a scale simply not available at smaller grid sizes. A single deduction in a well-chosen row can propagate through eight or ten columns, each confirming cells that in turn update further rows — a chain reaction covering thirty or forty cells from a single analytical step. These Japanese crossword and Griddler puzzles are among the most rewarding in the intermediate-large transition.

Medium 15×15: The 30-Line Management Challenge

With 30 lines competing for attention each pass, undisciplined processing is the primary obstacle to efficient Medium 15×15 solving. The correct approach is strict priority-sorted line management:

Priority tier 1 — Zero-slack lines: Any line whose clue minimum span equals 15. Entire arrangement forced — process first, propagate immediately to all 15 intersecting lines.

Priority tier 2 — Low-slack lines (slack 1–3): High-overlap lines that yield four or more confirmed cells each. Process second — their confirmations often cascade into tier-1 opportunities in intersecting lines.

Priority tier 3 — Medium-slack lines (slack 4–7): Process after tier 1 and 2 confirmations have been propagated. Many tier-3 lines that appeared unresolvable in pass 1 become tier-2 lines after pass 1 confirmations update their constraint states.

Priority tier 4 — High-slack lines (slack 8+): Defer until later passes when accumulated cross-referenced information has substantially reduced their effective slack. Processing these lines too early wastes effort — they yield little before their intersecting lines are partially resolved.

Segment Analysis at 15×15 Scale

Segment analysis on 15-cell lines is particularly powerful because the longer line length means confirmed empty cells create segments with more varied block-fitting possibilities. The key technique is multi-block segment assignment: when a 15-cell line with a three-block clue has been segmented into two or three regions by confirmed empty cells, assigning each clue block to the segment it must occupy — and then applying overlap analysis within that segment — often resolves four to eight cells simultaneously.

For example: a 15-cell line with clue "4 3 5" and confirmed empty cells at positions 6 and 13 creates segments of lengths 5, 6, and 2. The "5" block can only fit in the third segment (length 2 is too small); this immediately forces the "5" block to occupy positions 14–15, resolves its segment, and allows the remaining "4" and "3" blocks to be distributed between the first two segments with their own overlap analysis.

Next Steps

→ 15×15 Hard — full arrangement enumeration across 30 lines

→ 15×15 Expert — hypothesis cascades spanning 225 cells

→ 20×20 Medium — scale the same techniques to a 400-cell grid

Blocked on a specific line? The 15×15 Nonogram Solver identifies the segment or arrangement step that unlocks it.