Sumplete: rules, strategy, and free play
Sumplete is a 2023 logic puzzle that pairs row-sum + column-sum arithmetic with a single binary decision per cell: keep or remove. The grid starts pre-filled with numbers and an edge clue showing the target sum for each row and column. You delete cells until every row and every column sums exactly to its target. No new digits, no arithmetic with multiple operators — just keep-or-cross.
THE RULES
- Start with a pre-filled grid + row/column target sums. Every cell already shows a number. Each row has a target sum on its right edge; each column has a target sum on its bottom edge.
- Cross out cells until every row sums to its target. The remaining (un-crossed) cells in a row must add up to that row's target — exactly. No remainder allowed.
- The same rule applies to every column. A cell's keep/cross decision must satisfy BOTH its row's target AND its column's target.
- There are no other rules. No no-duplicate rule, no neighbour rule, no shape rule. Just sums. The deduction comes entirely from the row+column constraint interaction.
BEGINNER STRATEGY
- Match-the-target rows. If the un-crossed cells in a row already sum to exactly the target, every other cell in that row must be crossed. Conversely, if even crossing every cell still wouldn't bring the sum below the target, you've made a mistake.
- Identify must-keep cells. When a row's target is greater than the sum of all OTHER cells, the largest cell must be kept. Same trick works on columns. Cross-referenced, both constraints often force a single cell.
- Spot must-cross cells. If crossing a specific cell would leave a sum LESS than the target with no further crossings possible, that cell must be kept. Conversely, if keeping a specific cell would overshoot the target even after crossing everything else, that cell must be crossed.
- Work the most-constrained row or column first. Rows or columns where the target is very close to the sum-of-all-cells (or very far from it) have the fewest valid configurations. Solving those first cascades constraints onto less-constrained rows.
- Never guess. Sumplete has a unique solution by deduction. If you're guessing, look for an overlooked must-keep or must-cross from a row+column intersection.
COMMON MISTAKES
- Crossing cells before checking both row AND column. A cell that looks deletable from the row's perspective might be essential for the column's target. Always verify both axes before crossing — every cell sits at a row+column intersection.
- Assuming the largest number must be kept. Large numbers feel 'important' but can be legally crossed if the row/column has enough other cells to reach the target. Check the arithmetic, not your instincts about which numbers matter.
- Not checking rows or columns that are already satisfied. Once a row's un-crossed cells already sum to its target, every remaining un-crossed cell in that row is FORCED to be crossed. Many beginners stop evaluating 'done' rows and miss these free deductions.
- Working one axis at a time. Sumplete's power is the row+column intersection. After every cross, both the row AND the column update — check both immediately. Players who sweep row-by-row and then column-by-column miss the cascading constraints that come from working both simultaneously.
HOW TO THINK ABOUT IT
Sumplete is a deletion puzzle, not a placement puzzle. Your job is to reduce: cross out cells until the sums collapse to their targets. The productive mental posture is 'what must I cross to bring this row down to the target?' and 'what would happen to the column if I crossed this cell?' — both constraints run simultaneously. Every cell you force (whether kept or crossed) propagates instantly into its row and column, so fast constraint propagation is the key skill.
WHY THIS PUZZLE REWARDS YOU
Sumplete is GridJoy's most beginner-friendly arithmetic puzzle. Where Kakuro and Killer Sudoku demand mental-arithmetic combination work + grid-rule juggling, Sumplete asks ONLY for sum-matching. That single-axis reasoning makes it ideal for warming up before harder puzzles — and the daily-format brand (every player gets the same Sumplete each day) created strong viral traction on HN + r/sumplete in 2023. GridJoy implements both small (5×5) and medium (8×8) variants; both have unique solutions and serve well as a 'puzzle break' between deeper sessions.
VARIANTS
- Number Blocks. The filling counterpart — instead of deleting cells, you place digits into blank cells so each row and column hits its target sum. Same sum-matching goal, opposite operation.
- Kakuro. Each run of empty cells must sum to a given clue, with no digit repeating within a run. A step up from Sumplete — combination reasoning replaces simple residual arithmetic.
- Star Battle. A non-arithmetic grid puzzle where you place stars so each row, column, and region contains exactly N. Same 'select or exclude cells to satisfy row-column constraints' logic, but no sums involved.
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Deletion amounts, forced keeps/deletes, and why guessing breaks the puzzle.
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PLAY IT IN GRIDJOY — FREE ON ANDROID
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