How to Solve a Paint-by-Number Logic Puzzle on Web Paint-by-Number

To solve a puzzle on Web Paint-by-Number (webpbn.com), read each row and column clue as a list of filled-block lengths in order, then use overlap and elimination to mark cells that must be filled or must be empty. Start with the longest clues and the most constrained lines. You can finish a puzzle using logic alone—no guessing is required—if you work systematically and record what each line rules out.

What the numbers mean

Each clue is a sequence of numbers, and each number is the length of one continuous run of filled cells in that row or column. The runs appear in the same order as the numbers, and at least one empty cell separates consecutive runs.

• A clue of 3 means one run of three filled cells somewhere in that line.
• A clue of 1 2 means a single filled cell, then a gap, then two filled cells, in that order.
• A blank clue (no numbers) means the entire line is empty.

The order matters: 2 1 and 1 2 describe different arrangements, so you cannot reorder runs.

Use overlap to find cells that must be filled

The fastest early progress comes from lines where the clue is long relative to the line length. If the total of a clue plus its mandatory gaps is more than half the line, some cells are forced.

For a line of length 10 with clue 6: the run can start anywhere from position 1 to position 5. In every possible placement, positions 5 and 6 are filled. Mark those two cells, then extend from them.

For a line of length 10 with clue 4 4: the two runs plus one gap total 9 cells, leaving only 1 cell of slack. The first run must start at position 1 or 2, and the second must end at position 9 or 10, so the middle cells are forced empty and the outer cells are forced filled. Work out the minimum and maximum start position for each run; cells covered by every placement are filled.

Use elimination to mark cells that must be empty

Once a cell is confirmed filled, the cells immediately around it are constrained:

• A filled cell at the end of a run has an empty cell on the outer side (unless the run touches the border).
• If a run of length n is confirmed, the cell just beyond each end is empty.
• If a line's filled cells already account for all its clue numbers, every remaining cell in that line is empty.

Mark empty cells explicitly. On Web Paint-by-Number you can mark cells as empty (often with a different mark or color) so you do not reconsider them. Tracking both states—filled and known-empty—is what makes later lines solvable.

Work from the most constrained lines

Choose the next line by how much information it gives you, not by reading order:

1. Lines whose clue total plus gaps nearly equals the line length.
2. Lines with a single large number.
3. Lines where several cells are already filled or already empty, so the remaining options are few.
4. Lines crossing a row or column you just solved, because the new filled cells constrain them.

After each deduction, recheck the crossing lines. A single confirmed cell can unlock a column that was previously ambiguous.

A worked example

Take a 5×5 grid. Row 1 has clue 5, so all five cells in row 1 are filled. Column 3 now has at least one filled cell from row 1. If column 3's clue is 1, then the rest of column 3 is empty, which tells you row 2 through row 5 in column 3 are empty. Those empty cells then constrain the rows they cross. Each deduction feeds the next; this chain is the normal solving rhythm.

Verify before you finish

Check each completed row and column against its clue: count the runs, confirm their lengths and order, and confirm at least one empty cell between runs. A common error is treating two adjacent runs as one, or placing a run one cell off because a gap was not counted. If a line looks wrong, backtrack to the last cell you were unsure about rather than guessing elsewhere.

Common sticking points

• Forgetting the mandatory gap. When adding clue numbers, add one empty cell between each pair of runs. A clue of 3 3 in a line of length 6 is impossible because it needs 7 cells including the gap.
• Marking filled cells without marking empty ones. Empty marks are deductions too; leaving them unmarked causes repeated rechecking.
• Guessing too early. If a line has multiple valid placements, leave it and solve a more constrained line first. The puzzle is designed to be solvable by logic.
• Ignoring the borders. Runs at the edge of the grid have fewer placements, which often makes them the best starting point.

Once you are comfortable with overlap and elimination, most puzzles on the site become a matter of patience: solve the constrained lines, propagate the results to crossing lines, and verify each line as you complete it.