Mathdoku vs KenKen vs Calcudoku: What's the Difference — and How Do You Solve Them?

Mathdoku, KenKen, and Calcudoku are three names for the same puzzle: a Latin-square grid where each row and column holds every digit once, and outlined "cages" must hit a target number using a given operation. The names differ because "KenKen" is a registered trademark — the rules are identical.

What Is Mathdoku? (And Why It Has Three Names)

If you've searched for "KenKen" and ended up on a site called something else — or if a puzzle book says "Calcudoku" when you expected "Mathdoku" — you've run into one of the quirks of this puzzle's history.

The core mechanic was developed in Japan by math teacher Tetsuya Miyamoto, who invented the puzzle in 2004 as a classroom exercise to build arithmetic fluency. When the puzzle reached the US market, the name "KenKen" was trademarked by Nextoy LLC, which publishes it under that brand. Other publishers — free to use the same mechanic, since you can't trademark a puzzle format — chose different names: "Mathdoku" and "Calcudoku" are the two most common generic alternatives.

📝 A note on names: "KenKen" is a registered trademark of Nextoy LLC. "Mathdoku" and "Calcudoku" are generic names for the same puzzle mechanic. This article uses all three names in a comparative, informational context — we're not affiliated with or endorsed by Nextoy LLC or any KenKen publisher.

So the short answer to "what is Mathdoku?" is: it's KenKen, with a different label. The long answer is the rest of this article.

Mathdoku vs KenKen vs Calcudoku: Are They Really Different?

This is the question most people searching "mathdoku vs kenken difference" actually want answered — and the honest answer is: not in any meaningful way.

Here's a side-by-side comparison:

NameGeneric?Trademark?Where You'll Find It
KenKenNoYes — Nextoy LLCkenken.com, NYT Games
MathdokuYesNoFree puzzle sites, apps, printable books
CalcudokuYesNocalcudoku.org, puzzle apps, books

The rules, grid types, and solving logic are the same for all three. A 4×4 KenKen grid and a 4×4 Mathdoku grid are solved using identical techniques. The only meaningful differences:

  • Grid size choices vary by publisher. KenKen.com offers 3×3 through 9×9. Calcudoku.org tends toward 4×4 through 9×9. Mathdoku apps vary.
  • Operations offered can differ slightly — some "Mathdoku" implementations offer only addition and subtraction for beginners, while KenKen's full format uses all four (+, −, ×, ÷).
  • Brand polish differs — KenKen has dedicated apps, a New York Times partnership, and tournament events.

But the puzzle you're solving? Same puzzle.

Three names, one puzzle: Mathdoku, KenKen, and Calcudoku all refer to the same Latin-square arithmetic puzzle mechanic. Diagram showing three name badges — Mathdoku (generic), KenKen (trademark), and Calcudoku (generic) — each connected by an arrow pointing to a single 4×4 grid in the center, illustrating that all three names describe the same puzzle. 6+ 3− Latin-square + cages Mathdoku generic name Calcudoku generic name KenKen registered trademark Same rules. Same mechanic. Different publisher labels. Just for fun — not medical advice.
Three names, one puzzle — the rules don't change with the label.

How to Play Mathdoku: The Rules

Whether you're looking at a KenKen, Mathdoku, or Calcudoku puzzle, the rules are the same:

The Latin-square rule. Every row and every column must contain each digit exactly once. In a 4×4 grid, that means the digits 1, 2, 3, and 4 appear exactly once per row and once per column. In a 6×6 grid, it's 1 through 6. The grid size always determines which digits you use.

The cage rule. The grid is divided into outlined regions called "cages." Each cage shows a target number and an operation (for example, "6+" or "12×"). The digits inside the cage must produce that target using the given operation.

No repeats within a cage. Just as with Killer Sudoku's cages, you cannot use the same digit twice inside one cage — even if repeating it would hit the target.

Operations you'll see:

  • + The digits in the cage must add up to the target. (A "7+" cage in a 4×4 grid holds {3, 4} — the only pair that sums to 7 within digits 1–4.)
  • A 2-cell cage where the larger digit minus the smaller equals the target.
  • × The digits multiply to the target.
  • ÷ A 2-cell cage where dividing the larger by the smaller gives the target.

One-cell cages (a single cell with a number and no operator) are freebies — the digit is given directly.

How to Solve a 4×4 Mathdoku Step by Step

A 4×4 grid is the standard starting point for beginners. Let's walk through a concrete example. The grid uses digits 1–4 in every row and column.

4×4 Mathdoku example grid with four cages: 6+ top-left row pair, 2÷ top-right row pair, 3− bottom-left column pair, 8× bottom-right column pair. A 4×4 Mathdoku puzzle grid using digits 1 through 4. Top row: left two cells form the 6-plus cage outlined in teal, right two cells form the 2-divide cage outlined in amber. Rows 2 and 3: leftmost column cells form the 3-minus cage outlined in blue, rightmost column cells form the 8-times cage outlined in purple. Interior cells show example digits. Each cage label appears at its top-left corner. 4×4 Mathdoku — Example Grid Digits 1–4 in every row and column · cage targets at top-left 6+ 3− 2 3 4 1 col 1 col 2 col 3 col 4 r1 r2 r3 r4 6+ add to 6 2÷ divide to 2 3− subtract to 3 8× multiply to 8 Just for fun — not medical advice.
A worked 4×4 example. Cage targets sit in the top-left of each outlined region.

Step 1: Start with the most constrained cages.

The 3− cage contains two cells in the same column. In a 4×4 grid (digits 1–4), the only pair that subtracts to 3 is {1, 4}. That cage is solved immediately — write 1 and 4 in those two cells (row order determined by column constraints).

Step 2: Use the Latin-square rule to eliminate.

With 1 and 4 locked into that column by the 3− cage, those digits cannot appear anywhere else in the column. Cross them off candidate lists for every cage sharing that column.

Step 3: Resolve the division cage.

The 2÷ cage is a two-cell row cage: valid pairs in a 4×4 grid are {1, 2} and {2, 4}. If your column eliminations have already ruled out 1 in one of those cells, the pair is forced to {2, 4}.

Step 4: Use row elimination to close the grid.

Once three of the four cells in a row are filled, the fourth is forced — no arithmetic needed. The 8× cage (pair: {2, 4}) and 6+ cage (pair: {2, 4}, since 2+4=6 is the only valid pair in a 4×4 grid) resolve through the remaining row and column constraints.

The four habits to carry into every puzzle
  1. List all valid digit combinations for each cage first.
  2. Eliminate candidates using row and column constraints.
  3. Fill forced cells immediately — each one unlocks neighbors.
  4. Revisit cages after each fill; new constraints often resolve what looked ambiguous.
This elimination loop is the same logic Killer Sudoku uses — just on a smaller grid with more operation variety.

How Mathdoku Compares to Sudoku, Killer Sudoku, and Kakuro

Mathdoku sits in a family of logic puzzles that all use numbers, but each has a distinct mechanic:

Mathdoku vs Sudoku. Sudoku uses no arithmetic — it's pure placement logic. Mathdoku adds arithmetic operations to every cage, making it more arithmetic-forward. Beginners sometimes find Mathdoku's smaller grid (4×4 vs 9×9) less intimidating, even though the mental math is extra work. If you're looking to strengthen your Sudoku skills with a variation that adds arithmetic challenge, our guide on how to get better at Sudoku is a good companion read.

Mathdoku vs Killer Sudoku. These two are cousins. Both use cages with target sums and a no-repeat rule. The key differences: Killer Sudoku always uses addition (no multiplication or division), and it plays on a full 9×9 Sudoku grid with all the standard Sudoku row/column/box rules intact. Mathdoku uses a smaller standalone grid with multiple operation types. If you enjoy Mathdoku's cage arithmetic, Killer Sudoku is the natural next challenge — larger, addition-only, and embedded in a full Sudoku framework.

Mathdoku vs Kakuro. Kakuro is sometimes mistaken for a Mathdoku relative because both involve arithmetic in a grid. But the mechanics are quite different: Kakuro uses a crossword-shaped grid where digit runs (not cages) must sum to clue numbers printed in black triangles — there's no Latin-square rule, and no multiplication or division. The constraint is "no repeats within a run," not "every digit appears once per row." Kakuro is more about finding the right combination for each run's sum; Mathdoku is about balancing arithmetic against placement rules simultaneously. Our Kakuro guide covers the run-based solving method in detail.

All three — Killer Sudoku, Kakuro, and Mathdoku — belong to the broader family of cage and constraint puzzles. For a full map of where these fit, the logic puzzles for adults hub has an overview of the whole landscape.

Practice Your Cage Math — Try Make 10

The addition cages in Mathdoku — especially on a 4×4 grid — use the same number-bond skill that makes puzzle math click: knowing which small numbers combine to hit a target.

A "6+" cage with two cells needs {2, 4} or {1, 5} (if using digits 1–6). A "7+" cage needs {3, 4} or {1, 6} or {2, 5}. You're finding pairs that sum to a target — which is exactly what the Make 10 game is built around.

If you'd rather practice on paper, our free printable number bonds worksheets are designed around the same target-sum mechanic — print and solve at your own pace. These are genuinely useful warmups before you tackle a 6×6 Mathdoku.

Frequently Asked Questions

Is Mathdoku the same as KenKen?

Yes, in terms of rules. Both use a Latin-square grid with arithmetic cages. "KenKen" is a registered trademark of Nextoy LLC. "Mathdoku" is a generic name for the same puzzle mechanic. You'll solve them identically.

What is the difference between KenKen and Calcudoku?

The rules are identical. "Calcudoku" is another generic name for the same Latin-square arithmetic puzzle. Calcudoku.org uses that name; KenKen.com uses their trademarked brand. The difference is the publisher and the label, not the puzzle.

Is Mathdoku good for beginners?

A 4×4 grid is genuinely beginner-friendly. It uses only four digits, the cages are small (two to four cells), and each puzzle resolves in a handful of logical steps. The arithmetic is basic — single-digit addition, subtraction, and multiplication. Starting with addition-only cages before enabling all four operations is a reasonable progression if you find multiplication cages frustrating at first.

Where can I play Mathdoku for free?

Several sites host free daily puzzles under their preferred name: calcudoku.org (free daily puzzles), kenken.com (free puzzles with a branded KenKen format), and various puzzle apps offer Mathdoku as an unlabeled generic mode. No downloads or accounts are required on the free tiers of most of these. You can also print Mathdoku grids from free puzzle-generator sites if you prefer paper.

Ready to practice sum sense? Make 10 is open — a short number puzzle, no download, no account. A good warmup before a Mathdoku session.

More from the Make10s blog: how to play Killer Sudoku · how to solve Kakuro · how to get better at Sudoku · brain games like Sudoku · compare all logic puzzles · all posts

Source: KenKen — Wikipedia (history, trademark, and generic names).

About the author: Jay M. spent years in private education — including managing a coding academy branch and creating online educational content — before building Make10s as a free resource for adults who want to keep their minds active and engaged. The games and guides here are designed to be genuinely useful, not just eye-catching.

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