Kakurasu is a Japanese logic and math puzzle played on an N x N grid. Columns are weighted 1 through N across the top, and rows are weighted 1 through N down the left. Players mark cells so that the weights of marked cells equal the target sum shown at the end of each row and column.

How are cell values calculated in Kakurasu?

When a cell in column C is checked, it contributes C to its row's total sum. When that same cell in row R is checked, it contributes R to its column's total sum.

What should I do if a target sum is 0?

If a row or column has a target of 0, no cells in that row or column can be checked. Immediately mark every cell in that row or column with an 'X'.

What should I do if a target sum equals the maximum possible sum?

For a grid of size N, the maximum sum is 1 + 2 + ... + N (e.g., 15 for a 5x5 grid, 21 for a 6x6 grid). If a target equals this maximum value, every single cell in that line must be marked.

Can I solve Kakurasu without guessing?

Yes! All WaffleArcade Kakurasu puzzles have a unique solution that can be deduced logically using subset sum deduction, cross-referencing constraints, and elimination.

Kakurasu is a Japanese logic and math puzzle played on an N x N grid. Columns are weighted 1 through N across the top, and rows are weighted 1 through N down the left. Players mark cells so that the weights of marked cells equal the target sum shown at the end of each row and column.

How are cell values calculated in Kakurasu?

When a cell in column C is checked, it contributes C to its row's total sum. When that same cell in row R is checked, it contributes R to its column's total sum.

What should I do if a target sum is 0?

If a row or column has a target of 0, no cells in that row or column can be checked. Immediately mark every cell in that row or column with an 'X'.

What should I do if a target sum equals the maximum possible sum?

For a grid of size N, the maximum sum is 1 + 2 + ... + N (e.g., 15 for a 5x5 grid, 21 for a 6x6 grid). If a target equals this maximum value, every single cell in that line must be marked.

Can I solve Kakurasu without guessing?

Yes! All WaffleArcade Kakurasu puzzles have a unique solution that can be deduced logically using subset sum deduction, cross-referencing constraints, and elimination.

Logic Classic • Sum Grid

Kakurasu (Sum Grid)

Test your mental arithmetic and spatial deduction! Mark squares so the column and row index weights add up to exact target sums.

5x5 Index Arithmetic5x5 Grid • Easy

0:00

0 cells marked

Click Tool:

Row

1(0)

14(0)

5(0)

1(0)

10(0)

Col

8(0)

7(0)

5(0)

7(0)

TARGET

Left-click: mark / cycle • Right-click: cross (✕)Sum matches: 0/10

Balancing Kakurasu matrices...

Kakurasu Rules & How It Works

Kakurasu (also known as "Index Sums") turns simple addition into an intricate deduction matrix:

1. Column Weights (1 … N)The blue numbers across the top header assign weight C to each column. Checking a square in column 3 adds 3 to that row's sum.

2. Row Weights (1 … N)The amber numbers along the left header assign weight R to each row. Checking a square in row 4 adds 4 to that column's sum.

3. Exact Target TotalsThe target number on the right of each row and bottom of each column must be met exactly. Never exceed a target number.

4. Crossed (✕) EliminationMarking a cell with an 'X' prevents inadvertent clicks and helps visualize which remaining weights are still available.

Key Solving Techniques & Deductions

1. Zero and Maximum Extremes

Always inspect the puzzle edges first! A target of 0 allows you to cross out every cell in that row or column immediately. Conversely, a target equal to the triangular sum N × (N + 1) / 2 (such as 15 on a 5x5, or 21 on a 6x6) forces every cell to be checked.

2. Impossible Weight Elimination

If a row target is 3 on a 6x6 grid, columns 4, 5, and 6 can never be checked because any one of them would immediately overshoot the target 3! Immediately cross out (✕) all cells whose weight exceeds the target.

3. Near-Maximum "Missing Weight" Inversion

On a 5x5 grid (total sum = 15), if a target is 14, only one weight can be omitted: 15 − 14 = 1. That means column 1 is crossed out, and columns 2, 3, 4, and 5 must ALL be checked!

4. Subset Sum Uniqueness

Certain sums have only one unique partition. For instance, on a 5x5 grid, a target of 1 can only be {1}. A target of 2 can only be {2}. A target of 12 can only be {3, 4, 5} or {1, 2, 4, 5}. Cross-referencing with the orthogonal column restrictions will reveal the only valid combination.

Explore More Daily Pencil & Logic Puzzles

All 70+ games on WaffleArcade are completely free to play with no downloads or paywalls.

Nurikabe Islands Shikaku Rectangles Yajilin Arrow Loops Battleship Solitaire Akari (Light Up)