Sum puzzle strategy, where to start and how to solve it without guessing

September 26, 2026 · 6 min read · Tyamka team

A step by step way to solve a number grid where you remove numbers until every row and column hits its target, with a worked 4×4 example.

In a sum puzzle you get a grid of numbers with a target at the end of every row and every column. You remove numbers until what is left in each line adds up to its target. If you have played Sumplete, the idea is similar. This guide is about the order of reasoning, so that you never have to guess. The examples come from the sum puzzle online on this site, called Target Sums in the app.

The rules that matter for strategy

• Every row and every column has a target. The numbers left in the line must add up to exactly that.
• Exactly one set of numbers works. If a removal is not part of that set, it is wrong.
• In Target Sums a wrong removal costs one of three lives and the number stays. There is no undo, because the game only ever accepts a right removal.
• When a row or a column is finished, it gets a check mark and the numbers left in it are circled. Circled numbers stay, and the game will not let you remove them.
• The footer shows how many numbers you have removed out of how many have to go.

Lean on the second rule. Since the answer is unique, you can reach it by reasoning, though sometimes only by comparing several lines together. If you are about to guess, you have missed a line that already decides something.

Step 1. Work out the excess of every line

For each row and column, add up all its numbers and subtract the target. What you get is the excess, the exact amount you have to remove from that line.

On levels without negative numbers, a line with an excess of 0 is already finished. Nothing in it goes, and the game marks it done from the start.

Step 2. Start with the lines that have only one answer

Now look for the lines where only one group of numbers adds up to the excess. Three patterns come up again and again.

• A small excess. An excess of 1 in a line with a single 1 means that 1 goes.
• A number bigger than the excess stays. With positive numbers only, you cannot remove something larger than what has to go. In a row with an excess of 6, a 7, 8 or 9 stays.
• A small target. When the target is small, think about what stays rather than what goes. A column with the target 7 and the numbers 8, 7, 5 and 6 can only keep the 7, so the other three go.

Step 3. Carry each result across

Every cell belongs to one row and one column. When you settle a cell in a row, go straight to its column and recalculate what it still needs. Each line that becomes certain tends to settle the lines that cross it.

A worked example

This is a real 4×4 puzzle from level 3 of Target Sums. Five numbers have to go.

First, the excess of every line.

Row 2 and column 3 are finished before you touch anything. Now the reasoning.

1. Row 4, excess 6. The row holds 6, 9, 5 and 8. The 9 and the 8 are bigger than 6 and stay. The 5 alone is not enough. Only the 6 works, so the 6 in column 1 goes.
2. Column 2, excess 1. The only 1 in the column is in row 1. It goes.
3. Column 1, target 7. Think about what stays. The column holds 8, 7, 5 and 6, and the only way to be left with 7 is to keep the 7. So the 8 in row 1 and the 5 in row 3 go too.
4. Row 1. The 8 and the 1 are gone, which removes exactly 9, the excess. The row is done, and both of its 9s stay.
5. Row 3, excess 14. The 5 is gone, so 9 more has to go. The row has two 9s. The one in column 2 cannot go, because column 2 is already done, and the 7 stays because column 3 was done from the start. So the 9 in column 4 goes.
6. Check column 4. 9, 5 and 8 are left, which makes 22. Done.

Five removals, none of them a guess. Read alone, rows 1 and 3 had several possible answers, and only the crossing columns settled them.

When the numbers get small

Some levels use only small numbers, 1 to 5 on levels 5, 8 and 12, and 1 to 4 on level 13. Small numbers make many groups add up to the same total. In a row of 2, 3, 1, 4 and 2 with an excess of 5, there are four different ways to remove 5.

Lean harder on crossing lines, since a single line rarely decides anything, and use the small target trick from step 2 more often. When a line keeps only one or two numbers, there are far fewer ways to keep than to remove.

When some numbers are negative

On levels 9, 14 and 15 some numbers are negative. Removing a negative number makes the sum bigger, so the excess of a line can be negative, which means you have to remove negatives to raise the total.

Two shortcuts stop working.

• A number bigger than the excess can still go. A row with an excess of 3 might remove 5 and −2 together.
• Reaching the target does not mean the line is done. A row can add up to its target while a pair like +3 and −3 still has to go, because together they change nothing. Target Sums counts a line as done only when exactly the right cells are removed, so trust the check mark, not the sum.

The method itself stays the same. Start from the line with the fewest possible answers and use the crossing lines to rule options out until one remains.

Speed and points

Every right removal gives 10 points and a speed bonus of up to 10 more. The bonus drops by one for every second since your previous removal, so a removal in under half a second after the last one gets the full bonus, and from 9.5 seconds there is none. A wrong removal gives nothing and costs a life.

So think first, as long as you need, and once a chain of deductions is clear, make the removals quickly one after another. In the example above, steps 1 to 3 settle four of the five removals before you have tapped anything.

How the levels grow

The grid grows from 3×3 on level 1 to 6×6 from level 10, and roughly 30 to 50 percent of the numbers go. Levels 5, 8, 12 and 13 use small numbers only, and levels 9, 14 and 15 add negatives. Each puzzle is generated by the game, which checks that it has exactly one answer before showing it to you.

Where to go next

Try Target Sums, free up to level 5. If numbers are your thing, the mental math tricks cover the other number game on the site, and how to solve a maze covers the third logic game. All games are on the all games page.