MathDoku (KenKen)

One hidden Latin square, cut into arithmetic cages. Rebuild it before the clock — or the bot — beats you to it.

Updated July 16, 2026

KenKen in One Minute

Every MathDoku board on Scotix starts life as a fully solved Latin square — a grid where the digits 1 through N appear exactly once in every row and column. The game then chops that hidden solution into irregular blocks called cages, marked off with bold borders, and stamps each cage with a target number and an operator (6+, 2÷, 12×). A cage with only one cell just shows a bare digit, no symbol attached.

Your job is to reconstruct the Latin square the generator started with, using only the cage labels as clues. Two rules must hold at once: no digit repeats in any row or column, and every cage's filled cells combine with its operator to hit its target exactly. Get both right across the whole board simultaneously and every cell locks green — that's the win condition, checked fresh after every keypad tap.

Board size depends on who you're facing. Standard boards are 4x4 with a 120-second clock. Once your opponent's rating passes 1600 ELO, the game switches you to a 5x5 grid with a 180-second clock instead — more cages, more digits, more time to compensate. Controls are entirely click-based: select a cell, tap a number 1 through N on the side keypad, or hit CLEAR to empty it.

How Cage Arithmetic Works

The generator doesn't design cages by hand — it walks the finished Latin square and claims cells greedily. Starting from the first unclaimed cell, it rolls a target cage size: 15% of the time the cage stays a single cell, 65% of the time it grows to two cells, and 20% of the time it reaches for three, grabbing random orthogonal neighbors as it goes. If the walker paints itself into a corner — every neighboring cell already claimed by an earlier cage — it settles for whatever size it managed, even if that's smaller than the roll called for. That's why cages near grid edges are more likely to end up as lone singles.

Once a cage's cells are locked in, the operator gets picked from the actual solved digits sitting in those cells:

• Single-cell cages just display that cell's own solved digit — no operator, no ambiguity.
• Two-cell cages first roll a coin-flip attempt at division: if the two digits divide evenly, the cage becomes a ÷ cage. If they don't divide evenly (or the coin flip misses), the game cascades through further coin flips for - (absolute difference, which always works for any two distinct digits), then +, and falls back to × if nothing else lands first.
• Three-cell cages are a straight 50/50: either the sum of all three solved digits or their product.

One quirk worth knowing: the arithmetic check never cares whether a cage repeats a digit — only the row/column check does. A straight two-cell cage is always two orthogonally adjacent cells, which by definition share a row or a column, so a repeat there would already be illegal. But a bent, L-shaped three-cell cage can include two cells that share neither, and the Latin square rules allow those two to hold the same digit.

A Repeatable Solving Method

The same sequence works on every board, 4x4 or 5x5, so it's worth drilling into muscle memory:

• Sweep for bare-digit cages first. Roughly 1 in 7 cages generates as a single cell with no operator — that digit is already solved, so place it immediately.
• Click every remaining cage and read the Cage Helper. The side panel runs the exact same combinatorial search the generator uses internally, listing every legal digit set of the right length that satisfies that cage's operator and target.
• Attack division cages next. They tend to have the shortest candidate lists. Take a 2÷ cage on a 4x4 board: among digits 1-4, only two pairs have a 2:1 ratio — {1,2} and {2,4}. That's the entire Cage Helper output for that cage. If you can rule out one pair using row or column logic, the other pair is forced.
• Use partial row/column knowledge to prune longer lists. A 3-cell 6+ cage on a 4x4 board has exactly three valid sets: {1,1,4}, {1,2,3}, and {2,2,2}. If two of that cage's three cells sit in the same row or column, {2,2,2} is dead on arrival — a row can't hold the same digit twice — and you're down to checking whether the repeated 1 in {1,1,4} would land in that same row or column.
• Fill what's forced, then re-scan. Every digit you lock in shrinks the candidate lists for every cage sharing its row or column. Repeat the sweep until the board fills.

Grid Size and Difficulty

Board size isn't a setting you choose — it's read off your opponent's ELO the moment a match starts. Anything at or below 1600 gets you the standard 4x4 grid and 120-second clock. Cross 1600 and the board jumps to 5x5 with 180 seconds on the clock. In Practice mode you're always paired against the game's baseline bot at 1200 ELO, so Practice is permanently a 4x4 board — and since that bot never actually races you, only the clock is working against you.

Duel mode is different: matchmaking pairs you against a live opponent near your own rating, so the grid you see reflects how you're actually performing. Climb past 1600 ELO and 5x5 boards start showing up regularly.

The bot's own solve time follows a formula built into the game: max(25, 130 − (opponent ELO − 1200) × 0.08) seconds, then randomized by ±15%. A 1710-ELO opponent (the kind that also triggers a 5x5 board) computes to a base of about 89 seconds, landing anywhere from roughly 76 to 103 seconds in practice. Push the ELO higher and that number keeps shrinking toward the 25-second floor — a very strong bot finishes in as little as 21 to 29 seconds, no matter how large the board got. The status line under the bot's avatar hints at its progress, switching to "Resolving Sudoku rules..." partway through its solve and "Calculating final cages..." as it nears the end — treat that second message as your cue that time is short.

Breaking a Deadlock

Stuck with no cage offering an obviously forced digit? Re-open the Cage Helper on every unfinished cage and compare list lengths rather than target sizes — a subtraction cage with a big target can still have plenty of valid pairs, while an unassuming division cage might only have one or two. Work the shortest lists first.

Look for cages that share a row or column with each other. If cage A's candidate list and cage B's candidate list both touch the same row, a digit ruled out in one often rules out an option in the other — that's usually faster than staring at a single cage in isolation.

When nothing narrows further, fall back on the Latin square guarantee underneath the whole puzzle: every row and every column is secretly just the digits 1 through N in some order, because that's literally how the board was generated before it got cut into cages. If a row already has N−1 cells filled, the last cell is forced regardless of what its cage label says — fill it, then let that new digit cascade into the cages around it.

Don't ignore the clock while you're doing this. It turns urgent — a red "hurry" state with an audible tick — once you hit 10 seconds remaining. If you're in a duel and the bot's status line reads "Cage board verified," it has already finished; the match ends the instant that happens, and if the timer hits zero first the result is the same. Either way, a loss reveals the full solution with red borders so you can see exactly where you went wrong before your next match.

From Paper KenKen to Scotix

Classic pen-and-paper KenKen (the style popularized by Tetsuya Miyamoto and syndicated through Nikoli) usually runs much larger — 6x6 up through 9x9 is common in print — with no clock at all. Solvers work with pencil marks, jotting every surviving candidate digit into the corner of each cell and erasing them one by one as cages get resolved. Scotix compresses that experience: grids top out at 5x5, the keypad only accepts one committed digit per cell with no candidate-marking, and the Cage Helper panel does the pencil-mark bookkeeping for you on demand instead of cluttering the grid.

What Scotix adds that paper never had is pressure. Practice mode keeps the closest feel to solving on paper — a fixed 4x4 board and a clock, but no opponent pushing you. Duel mode turns it into a race: a real matched opponent is solving the same puzzle type on their own clock, and the match is scored as a binary win or loss rather than the quiet satisfaction of a completed grid. There's no partial credit for a mostly-solved board when the timer runs out.

If you want the deeper permutation-hunting techniques that don't fit in a quick reference — including how to handle cages that share more than one row or column — the full KenKen/MathDoku strategy guide walks through them step by step. For a different kind of arithmetic pressure, Speed Calc Duel strips away the grid entirely and tests raw calculation speed instead.

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