How to play Between Sums
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. Also known as Doppelblock, Double block, Sum between.
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.
Playing Between Sums on Puzzle Solvers
- Choose a size and a difficulty, then press New Puzzle.
- Tap a square, then a number or ■ on the pad (or type; 0 or space shades). ✎ switches to pencil notes.
- A sum turns green when its line is full and adds up, red when it doesn’t.
- Hint explains the next deduction — counting, sums and what fits between the shaded squares.
Using the Between Sums 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.
A worked example
On a 6×6 grid, a row sum of 10 means every number is between the shaded squares — so they are at the two ends.
A row sum of 4 on a 6×6: either a single 4 between them, or 1 and 3.
Strategies
- 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.
- Count the gap. The number of squares between the shaded ones fixes how many numbers add up to the sum.
Common mistakes
- Forgetting that numbers outside the shaded pair don’t count.
- Putting three shaded squares in a line.
- Repeating a number in a row or column.
Where it comes from
This puzzle type was invented in Germany in the 2000s and is a regular at international puzzle contests.
Frequently asked 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.
Keep going
- Play Between Sumsa fresh puzzle every time
- Between Sums Solverstep by step, every move explained
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