How to Solve Sumplete: The Surplus Method

Updated June 2026

Sumplete gives you a grid full of numbers and a target sum for every row and column. Your job is to cross out numbers so the ones you keep add up exactly to each target. Stare at it as an addition problem and it feels like guesswork. Flip it into a subtraction problem and it becomes a tidy chain of forced deletions. That flip is the whole guide.

Stop adding — start removing

Every line already contains all its numbers, so it almost always starts too big. The amount you must delete is fixed: it is the surplus — the current total of all numbers in that line minus its target. You are not hunting for which numbers to keep; you are hunting for a set of numbers that add up to exactly the surplus, and crossing those out. Reframing it this way shrinks the search dramatically.

Start with surpluses of zero

If a line's numbers already total its target, the surplus is zero: keep everything, cross out nothing. Mark every cell in that line as a definite keep. This is the strongest possible information because it instantly fixes cells in every crossing line. Scan for these free lines first, before any real thinking.

Small surpluses have few options

A small surplus is a gift, because so few combinations reach it:

• Surplus of 1 — only a single 1 can be removed.
• Surplus of 2 — only a single 2.
• Surplus of 3 — either a lone 3, or a 1 and a 2 together.

Hunt for lines with one or two obvious deletions and commit them. Each cross-out you lock in feeds the crossing lines, which usually exposes the next forced move.

Let rows and columns cross-check

Crossing out a cell lowers both its row and its column at the same moment. So a deletion forced by a row often completes a column for free, and a deletion forced by a column resolves a row. Bounce between the two directions: after you cross out a few cells, recompute the surpluses of the lines they touch. A column whose surplus has dropped to match a single remaining big number points straight at the next cut.

Use the keep-mark as a checklist

Mark cells you have proven must stay with the keep symbol, not just the ones you delete. When the grid gets busy, a proven keeper you have marked is a cell you will never cross out by reflex, and it constrains the surplus arithmetic in its line. Treat keep-marks and cross-outs as equally valuable deductions — both remove uncertainty.

Read the colour feedback

The target clue turning green means that line is exactly right; leave it alone. A clue turning red means you have crossed out too much and the remaining sum has dropped below the target — restore a cell, usually the largest-value one you just removed. Work toward a board where every clue is green; the reds and the plain numbers are your live to-do list.

A practical plan

1. Compute each line's surplus = current total − target.
2. Resolve surplus-zero lines first (keep all), then surplus-equals-one-number lines.
3. For each remaining line, find numbers summing exactly to the surplus.
4. After every cut, recompute the crossing lines and chase the new forced moves.
5. Mark proven keepers, and use the green/red clues as your checklist.

Solve Sumplete by surplus and the panic disappears. You are no longer testing combinations at random — you are reading off, line by line, exactly how much has to go.