THE SETUP
Sumplete shows you an N×N grid filled with digits. Alongside each row and column is a target sum. Your goal: delete some of the digits in each row and column so that the remaining digits sum to exactly the target. Deleted cells can be in any position — you don't need to keep a run intact, just hit the total.
One digit can be deleted or kept. Every row and column must hit its exact target. The puzzle has a unique solution — there's exactly one pattern of deletions that satisfies all row and column targets simultaneously.
THE KEY INSIGHT: COMPUTE THE DELETION AMOUNT FIRST
In Kakuro or Killer Sudoku, you reason about what to place. In Sumplete, you reason about what to remove. The first number to calculate for any row or column isn't the target — it's the deletion amount:
deletion amount = (sum of all digits in the row) − (target sum)
If a row contains 3, 7, 2, 5 and the target is 10, the deletion amount is (3+7+2+5) − 10 = 7. You need to delete digits that together sum to 7. You don't choose what to keep — you choose what to remove, and you know exactly how much removal is needed.
This is Sumplete's core mechanic, and it's more powerful than it first appears. If the deletion amount equals one of the digits in the row exactly, that digit must be deleted — forced move, immediately visible.
FORCED MOVES APPEAR IMMEDIATELY
Sumplete forces moves in a way that makes it accessible earlier than similar puzzles. Three forcing conditions occur frequently:
- Deletion amount = 0: the target already equals the row sum. Keep all digits. No decision needed.
- Deletion amount = sum of all digits: the target is 0. Delete everything in this row. No decision needed.
- Deletion amount equals one digit exactly: only one digit matches the deletion amount (and no subset of other digits sums to it). That digit is deleted. Immediate forced move.
These three cases resolve several rows and columns in any well-formed Sumplete puzzle before you've made a single decision. Find them first — they do more work than anything that follows.
CROSS-PROPAGATION — WHERE THE REAL SOLVING HAPPENS
Once a digit is determined (kept or deleted) in its row, that decision also constrains its column — the same digit can't be both kept in the row and deleted in the column; it's one cell, one fate.
Example: you determine that the 7 in row 2, column 4 must be deleted. The column-4 target now needs to be hit without that 7. Update column 4's deletion amount to reflect the 7 being gone, and re-check for newly forced moves in that column. Propagate horizontally then vertically, then back, in rounds.
This cross-row-column propagation is identical in spirit to Kakuro's cross-referencing technique: a constraint in one direction reveals information in the perpendicular direction. The mechanic is different (deletion vs placement), but the reasoning loop is the same.
HOW IT COMPARES TO KAKURO AND NUMBER BLOCKS
All three puzzles use row and column sum targets as the primary constraint. The differences:
- Kakuro: empty cells, distinct-digit runs, no Latin-square base. You place all digits from scratch. Harder to get started because the grid gives you nothing directly.
- Number Blocks: empty cells, digits 1–9 (repeats allowed), Latin-square-like uniqueness within runs. You fill an empty grid to match sum targets.
- Sumplete: pre-filled grid, deletions only, no digit uniqueness constraint. The grid hands you all the information — you subtract from it rather than build up to it.
For players new to arithmetic puzzles, Sumplete is often the most accessible entry point. The filled grid means the arithmetic is visible immediately — you compute deletion amounts from what's already there rather than searching for what could go there.
THE SOLVE ORDER
- Compute the deletion amount for every row and column (row sum − target).
- Find zero-deletion rows and columns (keep everything) and full-deletion rows/columns (delete everything). Apply immediately.
- Find rows/columns where the deletion amount equals exactly one digit. Delete that digit; propagate to its column/row.
- Re-check all affected rows and columns for new forced moves after each propagation.
- Repeat until solved. Most beginner and medium Sumplete grids resolve completely in 2–3 rounds without any guessing.