NoCharge

Enumerate the arrangements

Nonogram clue calculator

Enter a line length and clue runs. The calculator lists possible arrangements, marks cells forced in every one, and explains the arithmetic without solving the puzzle for you.

Category: Learning

Bottom line: For a single nonogram line, this tool lists every way the runs can fit, and marks cells that are the same in all arrangements. It is educational: it shows the pattern and the count, and does not solve a whole puzzle or spoiler the next clue.

One line at a time

Length and runs

Line length is total cells. Runs are entered as commas: 2,1 means a two-cell run, a gap, then a one-cell run.

How it works

Each clue number is a filled run. Neighboring runs need at least one empty cell between them, so the minimum span is the sum of the runs plus the number of separating gaps. The calculator enumerates placements in a single line and compares every valid arrangement for cells that always agree.

Worked example

For a five-cell line with clue 3, the arrangements are XXX.., .XXX., and ..XXX. X means filled and a dot means empty. The third cell is filled in all three arrangements, giving ??X??; the question marks remain unresolved.

Clues 2,2 need 2 + 1 + 2 = 5 cells. In a five-cell line only XX.XX fits. In a four-cell line no arrangement exists. This minimum-span check explains an impossible input before any whole-grid reasoning is needed.

What it cannot do

  • The tool handles one line of 1–25 cells and positive whole-number runs. It does not accept pre-marked cells or a zero clue for an entirely empty line.
  • Forced cells use all valid arrangements. At most 200 arrangement strings are displayed; the display limit does not narrow the deduction to those first 200.
  • It does not combine crossing rows and columns, prove a full puzzle has a unique solution, or reveal a saved NoCharge puzzle.
  • Large sets take more work to enumerate. Calculations run in this page and are not uploaded or stored.

FAQ

What is a nonogram run?

A clue number is the length of one filled run; runs appear in order with at least one empty cell between them. The calculator enumerates every placement of those runs in a line.

Does the calculator solve a puzzle?

No. It computes the possible arrangements of one row or column from its clue. Cross-referencing rows and columns to reach a unique grid is the puzzle itself.

Why does it show "all cells determined"?

When every possible arrangement shares the same filled or empty cell, that cell is forced. The calculator lists those determined cells but does not claim the whole line is solved.

Can it handle large lines?

Lines are limited to 25 cells. The tool enumerates all valid arrangements, displays at most 200, and states when the display is shortened. Forced-cell comparisons still use the full set; large sets can take longer to calculate.

Embed this tool

<iframe src="https://nocharge.net/tools/nonogram-clue-calculator/" width="400" height="640" title="NoCharge nonogram clue calculator"></iframe>
<p>Source: <a href="https://nocharge.net/tools/nonogram-clue-calculator/">NoCharge tool</a></p>

Next action

Try it with a game