Math Sudoku· Advanced

Goal

Fill an N×N grid with numbers 1 to N. Like Sudoku, no number can repeat in any row or column. Additionally, groups of cells called 'cages' must satisfy arithmetic constraints.

How to Play

  • Tap an empty cell to select it.
  • Use the number keypad to enter a value.
  • Each cage displays a target number and operation symbol in its top-left corner (e.g., 6+, 2−, 12×, 3÷).

What Is a Cage?

A cage is a group of cells outlined by a bold dashed border. The top-left corner shows a target number and an operation symbol. The numbers in the cage must produce the target using that operation.

6+26+42+4= 6 ✓

Operations

  • Addition (+): Can have multiple cells. The sum of all numbers must equal the target.
  • Subtraction (−): Always exactly 2 cells. The larger minus the smaller must equal the target.
  • Multiplication (×): Can have multiple cells. The product of all numbers must equal the target.
  • Division (÷): Always exactly 2 cells. The larger divided by the smaller must equal the target.
3+121+2=3 ✓
3−414−1=3 ✓
6×232×3=6 ✓
3÷626÷2=3 ✓

Single-Cell Cages

A cage with only one cell shows just a number with no operation symbol. That number is the answer — fill it in right away as a sure clue!

33

Row / Column Rule

No number may appear more than once in the same row or column. (Same rule as Sudoku)

OK1234✓
NG1224✗

Completed Example

Here is a completed 3×3 grid filled with 1–3. Check how each cage's operation is satisfied.

  • Each row and column contains numbers 1 to N exactly once.
  • Numbers in a cage must produce the target using the specified operation.
  • Single-cell cages show the answer directly.
5+1−2−6×231312123
  • 5+ cage: 2+3=5
  • 1− cage: 2−1=1
  • 2− cage: 3−1=2
  • 6× cage: 1×2×3=6

Tip

  • Start with single-cell cages to lock in certain numbers first.
  • Check which numbers are already placed in a row or column to narrow candidates.
  • Use memo mode to note possible candidates in each cell and avoid mistakes.
  • For multiplication cages, factoring the target helps narrow down candidates quickly.

Math Sudoku simultaneously trains arithmetic fluency and logical reasoning. Tracking multiple constraints engages working memory under significant cognitive load.

  • Miyake et al. (2000) - Unity and diversity of executive functions
  • Reiter & Thornton (2013) - Using KenKen to Build Reasoning Skills, Mathematics Teacher