What Is Kakurasu? Rules, Tactics, and a Worked Example

What is Kakurasu, exactly?

What is Kakurasu? It is a compact shading puzzle played on a square grid, from a gentle four by four up to a meatier nine by nine, where every cell carries a hidden weight based on its position. Numbers along the top edge label the columns from one upward, and numbers down the left edge label the rows the same way. Target clues then sit along the right side and the bottom. You do not write a single digit anywhere. Instead you decide, cell by cell, whether it should be shaded or left empty, and the shaded cells must make every clue total come out exactly right. That simple on or off choice is what makes Kakurasu so easy to pick up and so quietly addictive once the deductions start clicking together.

The rules of Kakurasu

The rules of Kakurasu fit in a few lines. Each column is worth its position counting from the left, so the first column is worth one, the second is worth two, and the pattern continues across the grid. Each row is worth its position counting from the top in the same way. The clue printed to the right of a row equals the sum of the column weights of the shaded cells in that row. The clue printed below a column equals the sum of the row weights of the shaded cells in that column. Your goal is to shade cells so that every row clue and every column clue is satisfied at the same moment. A well-made Kakurasu board has exactly one solution, which means you never need to guess if you keep reasoning from what the clues force.

Here is a quick worked example. Picture a four by four grid with columns worth one, two, three, and four from left to right. Say the top row shows a clue of six on its right edge. You need shaded cells whose column weights add up to six, and that can happen as two plus four, or as one plus two plus three. To choose, glance at the bottom clues. If the first column has a bottom clue of zero, then nothing in column one can ever be shaded, which instantly kills the one plus two plus three option. The top row is therefore forced to shade columns two and four. Each small deduction like this trims the possibilities elsewhere, and the real joy of Kakurasu is watching one fixed clue ripple outward and lock several cells into place at once.

Beginner tactics for Kakurasu

• Start with the extreme clues. A clue of zero means shade nothing in that line, while a clue equal to the full total of one plus two up to n means shade every cell in it.
• Rule out the heaviest cell early. If a row clue is smaller than the largest column weight, the rightmost cell in that row simply cannot be shaded.
• Hunt for clues with only one possible combination. Some totals can be built just one way, and those hand you certain, guess-free cells right away.
• Cross-reference every candidate. A cell has to satisfy both its row clue and its column clue, so use one direction to confirm or cancel the other.
• Work the corners first. A corner cell sits on two edge clues at once, so it is often the most constrained and easiest certainty on the whole board.

How Kakurasu compares to Sudoku

Kakurasu and Sudoku share the same heart: pure deduction with a single guaranteed answer and no lucky guessing required. The difference is the currency you count. Sudoku asks you to place each of nine symbols exactly once in every row, column, and box, while Kakurasu asks you to make weighted arithmetic sums line up. Both reward patient scanning and the discipline of writing down what must be true before what might be true. If the arithmetic side of Kakurasu appeals to you, you may also enjoy Math On, a calm number game from the same studio behind Shapedoku. And when you want that classic every-symbol-once feeling with a warmer, more magical mood, Shapedoku trades Sudoku digits for nine glowing shapes, so you solve by color and form instead of numbers. You can try the free solver and printable boards at shapedoku.com, or start playing at app.shapedoku.com.