Free weighted-sum logic puzzle

Play Kakurasu Online

Shade cells in the grid so that the weighted totals match the numbers around the edge. Each filled cell is worth its position, and the clues tell you what every row and column must add up to. It is a clean, friendly puzzle with one logical answer.

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Click a cell to fill it, again to mark it empty, once more to clear it. A filled cell adds its top weight to the row total and its left weight to the column total.

Generating a Kakurasu with a unique solution…

What is Kakurasu?

Kakurasu is played on a square grid where every cell is either shaded or left blank. Around the grid are clues: a number to the right of each row and a number below each column. Small weight labels along the top and the left edge show how much each cell is worth.

The columns are weighted 1, 2, 3 and so on from left to right, and the rows are weighted 1, 2, 3 and so on from top to bottom. When you shade a cell, it adds its column weight to that row's total and its row weight to that column's total. Your job is to shade exactly the cells that make every total match its clue.

  • Every cell is either shaded or blank.
  • A shaded cell adds its column number to its row's total.
  • A shaded cell adds its row number to its column's total.
  • The clue on the right is the target sum for that row.
  • The clue below is the target sum for that column.

How to read a row or column

Treat one line at a time. A row clue is simply the sum of the column weights of its shaded cells, so solving a row means finding which of the weights 1 to N add up to the clue, using each weight at most once.

That makes the extremes very easy. A clue of zero means the whole line is blank. A clue equal to the maximum — 1+2+...+N — means the whole line is shaded. Clues just below the maximum are almost as strong, because only a small weight can be missing.

  • Clue 0: every cell in the line is blank.
  • Clue equal to the maximum: every cell is shaded.
  • A clue of N can be a single cell in the last column, or a combination.
  • Large clues force the high-weight cells near the far edge.
  • Small clues force the low-weight cells near the near edge.

The core technique: unique sums

Because each weight from 1 to N can be used at most once in a line, many clues break down in only one way. A row clue of 1 must be the cell in column 1; a clue of 2 must be column 2; a clue of 3 could be column 3 or columns 1 and 2 together. Spotting the forced decompositions first gives you a foothold.

Then let the rows and columns talk to each other. Shading a cell to satisfy a row also commits a value to its column, and the column clue may confirm or forbid it. Working a tight row against a tight column is where Kakurasu puzzles are won.

More ways to deduce

Look for the largest weight in a line. If the row clue is smaller than the last column's weight, that far cell must stay blank; if the clue cannot be reached without it, it must be shaded. The same reasoning runs down the columns with the row weights.

Marking cells you have ruled out is just as useful as shading the ones you are sure of. As the clues turn green one by one, the remaining cells are squeezed until the whole grid is forced.

Difficulty levels and why play online

Easy Kakurasu uses a 5x5 grid, where the sums are small and the forced cells are easy to spot. Medium moves to 6x6, Hard to 7x7, and Expert to a 8x8 grid where the totals are larger and the chains of deduction run longer.

Playing online does the adding for you: the row and column clues turn green the instant they are satisfied and red if you overshoot, mistaken cells show clearly, and your progress saves locally in your browser. Every grid is checked for a single solution, so a Kakurasu always rewards careful counting over guesswork.

  • Easy: a 5x5 grid with small, friendly sums.
  • Medium: a 6x6 grid for everyday play.
  • Hard: a 7x7 grid with longer deductions.
  • Expert: an 8x8 grid for confident solvers.

FAQ

Kakurasu FAQ

What is Kakurasu?

Kakurasu is a logic puzzle where you shade cells in a grid so that weighted sums match the clues. A shaded cell adds its column weight to its row's total and its row weight to its column's total.

What do the numbers around the grid mean?

The numbers on the right are the target sums for each row, and the numbers below are the target sums for each column. The small numbers on the top and left show how much each cell is worth.

How is a row or column total calculated?

Add up the weights of the shaded cells. In a row you add the column numbers of the shaded cells; in a column you add the row numbers of the shaded cells.

What does a clue of 0 or the maximum mean?

A clue of 0 means the whole line is blank. A clue equal to 1+2+...+N means the whole line is shaded, since every cell must be used to reach it.

Is there always a unique solution?

Yes. Every Kakurasu here is generated and checked so the clues lead to exactly one shading, so you can always solve it by logic alone.

Is the Kakurasu game free?

Yes. You can play online for free without signing up, on phones, tablets and desktop, and your current puzzle is saved locally in your browser.