Between Sums Solver

Between Sums Solver — Step by Step

Click a place left of a row or above a column and type its sum, then press Solve. Or play a generated puzzle and send it here with one click.

Between Sums Solver: rules, how to use it, tips

Shade two squares in every row and column and write 1 to N−2 in the rest, so each outside number is the sum of the numbers between that line’s two shaded squares.

The rules

Each row and column has exactly two shaded squares.
The other squares of each row and column hold the numbers 1 to N−2, each exactly once.
A number outside the grid is the sum of the numbers between the two shaded squares of that line.
A sum of 0 means the two shaded squares are next to each other.

Using the solver

Choose the size and type the sums (or press Sample).
Press Solve and step through: each number once, two shaded per line, and the sums.

Tips

Total sum. All the numbers in a line add up to a fixed total (10 on a 6×6). A big sum means the shaded squares are near the ends.
Zero. A 0 sum: the two shaded squares touch — find where a pair fits.
Combinations. List the sets that make a sum: on a 6×6, 7 is 3+4 or 1+2+4.
Each number once. Use rows and columns together like a sudoku.

The full guide, with a worked example and common mistakes: How to play Between Sums.

Questions

What does a sum of 0 mean?

The two shaded squares in that line are side by side, with nothing between them.

Do the shaded squares count?

No — only the numbers strictly between them are added up.

Is there always one answer?

Yes — every puzzle here is checked to have exactly one solution.

How do I solve one from a book?

Open the Between Sums Solver, type the sums and press Solve.