WHAT THEY SHARE
Both puzzles are Latin squares: fill an N×N grid so every row and column contains each digit from 1 to N exactly once. The uniqueness rule — no digit repeating in any row or column — is identical. Naked singles and hidden singles work in both puzzles.
Neither puzzle requires arithmetic in the true sense. In Sudoku the digits 1–9 are labels, not values. In Calcudoku the cage targets require you to find digit combinations — but the solving logic is constraint-elimination, not arithmetic computation.
THE KEY DIFFERENCE: CAGES REPLACE GIVEN DIGITS
Sudoku starts with 17–35 cells pre-filled with specific digits. Every given cell tells you exactly what one cell contains. Calcudoku starts with a mostly empty grid where the cells are grouped into outlined cages. Each cage shows:
- A target number (e.g. 12, 5, 3)
- An operator: + − × ÷ (sometimes omitted on easy grids)
Your job: place digits so that the digits in each cage combine with the given operator to reach the target. A cage reading "12×" with three cells might contain 2, 3, 2 (since 2×3×2=12) — or 1, 4, 3 (1×4×3=12). You find the valid combination through constraint elimination, just as you eliminate candidates in Sudoku.
SIDE BY SIDE
Grid structure
Sudoku: 9×9 with nine 3×3 boxes
Calcudoku: typically 4×4 to 9×9 (no box constraint)
Starting information
Sudoku: given digits in specific cells
Calcudoku: cage outlines + target + operator (no given digits)
Box constraint
Sudoku: yes — row + column + 3×3 box uniqueness
Calcudoku: no — only row and column uniqueness
Arithmetic involved
Sudoku: none — digits are labels
Calcudoku: light — cage combination enumeration
Grid size flexibility
Sudoku: always 9×9
Calcudoku: any N×N from 4 to 9+ (difficulty scales with size)
First move
Sudoku: scan for naked singles (cells with one candidate)
Calcudoku: enumerate cage candidates, find single-cell cages
THE CALCUDOKU FIRST MOVE
In Sudoku, the first forced placement comes from scanning rows, columns, and boxes for cells where only one digit fits as a candidate. Given cells are the anchor.
In Calcudoku, the first move comes from cage analysis. Single-cell cages are immediate placements — a cage with one cell and target "7" simply places a 7. Two-cell cages with subtraction or division often have very few valid combinations, giving you two candidates per cell from the start.
The key Calcudoku technique is enumerating the valid digit combinations for each cage, then cross-referencing with row/column constraints to eliminate impossibles. A 3-cell cage reading "6+" in a 4×4 grid has only a handful of valid 3-digit combinations from {1, 2, 3, 4} — finding them first is the Calcudoku equivalent of noting all candidates.
WHAT TRANSFERS FROM SUDOKU
The uniqueness constraint and elimination mindset transfer directly. Naked singles, hidden singles, and candidate elimination all work identically. Once you've found which digits can appear in each cell, the rest of the solve uses exactly the same logic as Sudoku.
The instinct to look for the most constrained cells carries over too. In Calcudoku, the most constrained cells are those in small cages (1 or 2 cells) with restrictive targets — the same way Sudoku's most constrained cells are those with fewest candidates.
Experienced Sudoku solvers adapt to Calcudoku quickly at beginner difficulty. The cage-combination step takes one or two puzzles to internalize; the rest is familiar elimination logic.
WHAT DOESN'T TRANSFER
Sudoku's 3×3 box constraint — the source of pointing pairs, box-line reduction, X-wings, and most advanced Sudoku techniques — doesn't exist in Calcudoku. Calcudoku is purely a row-column puzzle, so none of those box-dependent techniques apply.
Calcudoku introduces cage combination enumeration as a first step that Sudoku never requires. Before you can eliminate candidates in a cage, you must identify all digit combinations that satisfy the target and operator. For multiplication cages this means factoring; for subtraction and division cages it means identifying ordered pairs. The first Calcudoku puzzle typically takes twice as long as expected while this enumeration step becomes automatic.
WHICH IS HARDER?
At small sizes (4×4, 5×5), Calcudoku is faster and easier than 9×9 Sudoku. The grid is smaller; single-cell and two-cell cages provide immediate placements; the cage combination step is quick.
At large sizes (8×8, 9×9), Calcudoku is genuinely harder than equivalent-difficulty Sudoku for most players. The cage enumeration step compounds: a 9×9 Calcudoku with 4-cell multiplication cages can require holding large sets of candidate combinations in mind before any cell resolves. The absence of the box constraint also means fewer cascading forced moves — Sudoku's triple constraint (row + column + box) fires elimination chains faster than Calcudoku's double constraint.
A NOTE ON KenKen AND MATHDOKU
KenKen is Calcudoku under a registered trademark (Nextoy / Gakken). Mathdoku is another generic name for the same puzzle. GridJoy calls it Calcudoku — the non-trademarked name most widely used in puzzle competitions and academic research. The rules are identical regardless of the name. If you've played KenKen before, you'll recognise every rule in GridJoy's Calcudoku immediately.
WHEN TO MAKE THE SWITCH
If you play Sudoku: try Calcudoku when you want to keep the row/column elimination framework but add a new entry step — cage combinations. The solving logic is familiar; the new skill is enumeration rather than scanning. Start at 5×5 or 6×6, not 9×9.
If you play Calcudoku: try Sudoku when you want the third constraint layer (the 3×3 box) and the elimination chains it produces. Sudoku's box constraint is the one thing Calcudoku doesn't have — and it unlocks a whole family of techniques (pointing pairs, X-wings) that change how hard grids resolve.