All Sudoku Variants
9×9 · Arithmetic

Killer Sudoku Pro

Also known as Killer Pro, Mystery Killer

Killer cages whose clue can use any of the four operations — addition, subtraction, multiplication or division — not just sums.

5 3 6 7 2 915×1−

An example Killer Sudoku Pro puzzle: each cage hits its target under its operation — 5 × 3 = 15, and 7 − 6 = 1.

Killer Sudoku Pro extends Killer Sudoku from addition to all four operations. Each cage carries a target and a symbol — +, −, × or ÷ — and the cage's digits must produce that target under that operation. As in Killer, a cage never repeats a digit; the extra operations simply give the setter more ways to constrain it.

The rule: reach the target by the operation

Read each cage's clue as "target, then operation". A "12×" cage means its digits multiply to 12; a "5−" cage means they subtract to 5; a "3÷" cage means they divide to 3. Below, a two-cell "12×" cage holds 3 and 4, since 3 × 4 = 12.

3 412×

A "12×" cage: the digits multiply to 12 — here 3 × 4.

A worked example, step by step

Take an empty two-cell cage marked "12×".

12×

Step 0. A two-cell cage whose digits multiply to 12.

Step 1 — factor the target. Which two different digits multiply to 12? Only 2 × 6 and 3 × 4. (1 × 12 is out — 12 is off the grid.) So the cage is {2,6} or {3,4}.

2346234612×

Step 1. The cage is {2,6} or {3,4} — both cells drawn from {2,3,4,6}.

Step 2 — let the grid choose. Now the ordinary rules decide between them: if the cage's row or box already holds a 3, the {3,4} option is out and the cage must be {2,6}. One crossing digit usually settles the whole cage.

The operations, at a glance

Each symbol has its own flavour. Addition behaves exactly like Killer. Multiplication is about factors, so it loves the composite targets (12, 24, 36). Subtraction and division usually apply to two-cell cages and give a difference or ratio — a "2÷" cage is 1-2, 2-4, 3-6 or 4-8. Because subtraction and division aren't order-sensitive here (you take the larger over or minus the smaller), they behave much like the ratio dots of other variants.

Solving strategy

  • Match the method to the symbol. Sum cages use combinations; product cages use factors; difference and ratio cages have short, memorable lists.
  • Learn the small products. 12 = 2×6 or 3×4; 24 = 3×8 or 4×6; these recur constantly.
  • Let crossing units decide. Once a cage is down to two options, a single row, column or box digit usually picks one.
  • Feed the grid. Each digit a cage fixes behaves like a given for its row, column and box.

Common mistakes

  • Assuming addition. Check the symbol — a "12×" cage is nothing like a "12+" cage.
  • Allowing a repeat. As in Killer, a cage's digits are all different.
  • Forgetting off-grid factors. For products, ignore factors above 9 (12 can't use a 12).
  • Ignoring ordinary Sudoku. Cage cells still obey their rows, columns and boxes.

Can I play it here?

Not yet — Killer Sudoku Pro isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile: