THE CORE MECHANIC
Each row has a target sum shown on its right edge. Each column has a target sum shown at its bottom (or top). Clue cells are pre-filled; empty cells need exactly one digit from 1–9.
Unlike Sumplete, you're not removing numbers — you're adding them. Unlike Sudoku, there's no uniqueness constraint per row or column (the same digit can appear multiple times in a row). The only constraint is the sum target.
ONE EMPTY CELL = FORCED DIGIT
This is the most powerful technique in Number Blocks. When a row has only one empty cell left, its value is exactly:
digit = row_target − sum_of_all_filled_cells_in_row
No options, no guessing. Do the subtraction and write the digit. The same applies to columns. And because the digit goes into a specific cell, it simultaneously satisfies both the row and the column that cell belongs to — potentially reducing another row or column to its own single-empty-cell state.
PROPAGATE FROM FORCED CELLS
The solving loop works by cascade. One forced digit in a row removes an unknown from that cell's column. If the column now has only one empty cell, that digit is also forced. Filling it removes an unknown from its row. And so on.
In well-designed Number Blocks puzzles, this cascade resolves most or all of the grid. The puzzle is designed so deduction is always possible — you never need to guess.
After placing any digit, immediately recheck the row and column it belongs to. One placement often forces the next.
WHEN NO ROW OR COLUMN IS FULLY CONSTRAINED
If no row or column has a single empty cell, you need a secondary technique. Look for rows or columns with two empty cells and a narrow valid-pair range.
For a row with two empty cells (A and B) and a remaining sum of R (target minus filled cells):
- A and B must be digits 1–9 with A + B = R.
- If R ≤ 3, the only solution is (1, 2) or (2, 1) — very constrained.
- If R = 18, the only solution is (9, 9) — both cells are forced.
- For each candidate pair, check if the column targets allow those values. Pairs eliminated by column constraints narrow the options further.
THE SOLVING LOOP
- Scan every row and column. Find any with exactly one empty cell.
- For each one-empty-cell row/column: compute the forced digit (target − sum of filled cells). Write it in.
- After writing each digit, re-scan the cell's row and column for new one-empty-cell cases.
- When no one-empty-cell cases remain: find the most constrained two-empty-cell row/column and enumerate valid pairs, filtering by column (or row) targets.
- Repeat until the grid is filled.
THE BEGINNER MISTAKE
Scanning from the top-left and trying to fill cells in reading order. This ignores the structure of the puzzle. Always lead with the most constrained row or column — the one where the fewest cells remain empty. Constraint density, not grid position, tells you where to start.