About 3D Sudoku
The Concept: This puzzle expands standard Sudoku into a 9x9x9 matrix. Every single layer across all three dimensions (X, Y, and Z) is a complete, interlocking 9x9 Sudoku puzzle, creating 27 simultaneous games. Every cell sits in three rows, three columns and three 3x3 boxes at once.
Difficulty: Pick a level on the menu before starting. For the cube, Easy leaves about 200 of the 729 cells filled, Medium about 130, Hard about 85, and Master only about 55. Every puzzle is verified to have exactly one solution. Hard and Master puzzles cannot be finished plane by plane; you must use clues from the crossing planes. Master cubes take a few seconds to generate.
The Masking Effect: If you solve the outer faces (Planes 1 and 9) first, they form a solid shell that hides the inner cubes. To prevent this, completed outer planes turn a lighter, translucent green, allowing you to see inside.
Auto-Save & Resuming: Your progress is automatically saved by your browser in the background. You can return later and click RESUME GAME to pick up exactly where you left off. Note: Depending on your browser, this automatic resume feature may not carry over to Incognito or Private browsing windows. For a permanent, shareable backup of your 3D puzzle, use the manual EXPORT and IMPORT buttons.
The Math (2D): Generating a puzzle relies on the Exact Cover problem. Letting Xi,j,k = 1 if digit k is in row i, col j, the algorithm satisfies four constraint groups. For example, the row constraint is:
Σ(j=1 to 9) Xi,j,k = 1
A 9x9 grid has 729 candidate variables and 324 constraints. There are 6,670,903,752,021,072,936,960 valid 9x9 grids (about 6.7 × 1021).
The Math (3D): The cube has 729 cells and 6,561 candidate variables Xx,y,z,k. Each cell lies on 3 lines and in 3 boxes, so a single digit placement must satisfy seven constraint groups at once (one cell, three lines, three boxes), for a total of 5,103 exact-cover constraints across 486 rows, columns and boxes. Every cell has 36 peers it must never match, giving 13,122 mutual-exclusion relations.
The number of ways to fill 729 cells with digits 1-9 is 9729, roughly 10695. For comparison, there are about 1080 atoms in the observable universe. Checking all of them at a billion per second would take longer than 10678 lifetimes of the universe. The app does not do that. It builds a valid lattice algebraically in under a millisecond, then removes cells one at a time. After each removal it runs a complete depth-first search with bitmask constraint propagation and hidden-single detection, exploring the entire remaining solution space to prove the cube still has exactly one answer. A Master cube requires roughly 680 such full proofs and tens of thousands of search nodes, all in the time it took you to read this sentence.
You, meanwhile, have to do it with a pencil.
Credits: Original game by Ted with Gemma. 3D lattice engine, uniqueness solver, difficulty tiers and generation console by Claude Fable 5.1 (Anthropic), September 2026.
A Short History: The puzzle's ancestor is the Latin square, studied by Leonhard Euler in 1782: an n×n grid where each symbol appears once per row and column. Number puzzles built on 9x9 Latin squares appeared in French newspapers in the 1890s, but the modern game was invented by Howard Garns, a retired architect from Indiana, and published by Dell as "Number Place" in 1979. Japan's Nikoli company imported it in 1984 and named it Sudoku ("single numbers"), adding the rule that clues be arranged symmetrically. In 1997 Hong Kong judge Wayne Gould saw a partly finished puzzle in a Tokyo bookshop and spent six years writing a program to generate them; he convinced The Times of London to print one in November 2004, and within a year Sudoku was in newspapers worldwide. The first World Sudoku Championship was held in Lucca, Italy in 2006. 3D and cube variants followed soon after, though a full 9x9x9 in which every plane in all three directions is a valid grid, as here, remains a rare beast.
Fun Fact: The name "Sudoku" is a Japanese abbreviation of the phrase "Sūji wa dokushin ni kagiru", which translates to: "the digits must remain single."