Each cell is worth its row weight and its column weight, fill the right ones so every line's totals hit their targets exactly.
Kakurasu is a weighted-sum logic puzzle. The numbers along the top label each column 1, 2, 3… and the numbers down the left label each row the same way. A filled cell contributes its column number to that column's total and its row number to that row's total.
Every row has a target clue on the right and every column a target clue along the bottom. Choose which cells to fill so that each row's filled column-weights add up to its clue, and each column's filled row-weights add up to its clue. There's a single unique solution.
Kakurasu belongs to the tradition of Japanese-style logic puzzles built on arithmetic constraints, and like many puzzles that spread through magazines and the early web it carries no documented inventor or first publication.
Its clear ancestor in spirit is kakuro, where the clues are sums that a run of cells must reach. Kakurasu keeps the summing but changes what is being added: position itself becomes the value.
That is the idea worth noticing. A cell is worth its column number along its row and its row number down its column, so the same square contributes two different amounts depending on which total you are checking — which makes it a genuine constraint satisfaction problem rather than a filling exercise.
Kakurasu is a weighted grid logic puzzle solved entirely by arithmetic deduction, each board guaranteed to have one unique solution. This is an original, free browser version with three sizes plus daily and practice puzzles, playable instantly with no download or sign-up.