Killer Sudoku – Medium

Solving Killer Sudoku: Rules and Strategies

Killer Sudoku is a Sudoku variant. Dashed cages combine classic Sudoku logic with given sums.

Killer Sudoku is also known as Sum Sudoku or Sumdoku.

The numbers of a cage add up to the small cage sum and do not repeat within the same cage.

The goal is a completely and correctly filled puzzle. Each entry must be derived from the visible clues and the already placed numbers.

Rules

• Each cell contains exactly one number from 1 to 9.
• Each row contains the numbers 1 to 9 without repetition.
• Each column contains the numbers 1 to 9 without repetition.
• Each normal 3×3 block contains the numbers 1 to 9 exactly once.
• The numbers of a cage add up to the small cage sum and do not repeat within the same cage.
• Given numbers are not changed.
• Every entry must satisfy all rules.

Orientation within the grid

Rows are counted from top to bottom, columns from left to right. In (4,7), 4 is the row and 7 is the column.

The images show specific intermediate states. Blue marked fields are used for the step, red means excluded, and green indicates a secure result.

Basic solving idea

Calculate small cage combinations, residual values, and 45-sum relationships; then always check row, column, and block.

After each secure entry, recheck the affected row, column, block, and all additional clues. Often this already reveals the next step.

1. Close an almost complete row

In row 1, only cell (1,1) is empty. The numbers 1, 2, 3, 4, 6, 7, 8, 9 are already present. Therefore, only 5 is missing.

So, 5 is in (1,1). All other numbers are already in row 1.

2. Close an almost complete column

In column 1, only cell (1,1) is empty. The numbers 1, 2, 3, 4, 6, 7, 8, 9 are already present. Therefore, only 5 is missing.

So, 5 is in (1,1). All other numbers are already in column 1.

3. Close an almost complete region

In the 3×3 block 1, only cell (1,1) is empty. The numbers 1, 2, 3, 4, 6, 7, 8, 9 are already present. Therefore, only 5 is missing.

So, 5 is in (1,1). All other numbers are already in 3×3 region 1.

4. Calculate the residual sum of a cage

The marked cage sums to 16. Its known values total 11; only (1,1) is open.

16 − 11 = 5. Therefore, 5 goes in (1,1).

5. Form cage combinations without repetition

The cage with 2 cells requires a sum of 9. Only combinations of different numbers reaching this sum are allowed.

At the checked solution state, the cage contains 6 + 3 = 9. Order and exact positions are also determined by row, column, and block.

6. Apply the 45 rule to one unit

Every complete Sudoku row, column, and 3×3 block contains 1 through 9 and sums to 45. In column 1, the sum of fully contained cages is 34; the already visible remaining cells sum to 6.

Exactly one unknown remains: 45 − 34 − 6 = 5. So, 5 is in (1,1).

7. Check row, column, and region together

For (1,1), row, column, and region must be checked simultaneously. All numbers except 5 are excluded.

Therefore, only 5 remains in (1,1). Always check all related areas for an open cell.

Typical solving process

1. Start with small or extreme cage sums.
2. Calculate missing cage values and possible combinations.
3. Use the 45 sum for rows, columns, and 3×3 blocks.
4. Check each combination against the normal Sudoku units.
5. Update affected cages after each entry.

Common mistakes

• Repeating numbers in a cage: A cage combination uses different digits.
• Only check the sum: Each cage number must also fit into row, column, and block.
• Rushing to guess: If multiple numbers are possible, the cell is not yet solved.
• Not rechecking after an entry: A new number can immediately solve other cells.

Tips for beginners

• Start with rows, columns, blocks, or clues with few open fields.
• Write down possible numbers if you can't keep them in your head.
• Check each possible number against all rules of the cell.
• An eliminated possibility is also progress.
• If stuck, switch targetedly between rows, columns, blocks, and additional clues.

Solve Killer Sudoku in small, secure steps. After each entry, recheck the affected row, column, block, and additional clues. This way, you often reach the goal without guessing.