Mini Kropki squeezes the elegant dot logic of Kropki Sudoku onto a 6x6 grid with the digits 1 to 6. A white dot between two cells means their digits are consecutive; a black dot means one is double the other; and — the rule that makes Kropki special — no dot means neither. Many Mini Kropki grids start completely empty: the dots alone determine the unique solution, which makes every solve feel like decoding a message.
What is Mini Kropki Sudoku?
Kropki (Polish for "dots") replaces most given digits with relationship clues on the borders between orthogonally adjacent cells. Mini Kropki plays it on the 6x6 grid with 2x3 boxes, and the shrink transforms the difficulty: the pair tables that experts memorize for the 9x9 version become tiny on six digits. Three black-dot pairs. Five consecutive steps. That's the whole vocabulary — you can learn it in one puzzle.
Mini Kropki Rules
- Standard Mini Sudoku rules: Every row, column, and 2x3 box must contain the digits 1–6 exactly once.
- White dot rule: Cells joined by a white dot hold consecutive digits — they differ by exactly 1.
- Black dot rule: Cells joined by a black dot hold digits in a 2:1 ratio — one is exactly double the other.
- No-dot rule: Adjacent cells with no dot between them are neither consecutive nor in a 2:1 ratio.
Every Dot Pair on a 6x6 Grid
| Clue | Valid Pairs (digits 1–6) |
|---|---|
| White dot (consecutive) | 1-2, 2-3, 3-4, 4-5, 5-6 |
| Black dot (2:1 ratio) | 1-2, 2-4, 3-6 |
| No dot | Any pair that is neither consecutive nor 2:1 — e.g. 1-4, 2-6, 3-5, 1-5, 2-5, 4-6, 1-3, 1-6 |
Two immediate consequences worth memorizing: the digit 5 never touches a black dot (10 is off the grid, and 2.5 isn't a digit), and a cell caught between two black dots is almost always a 2 (the only digit that doubles one neighbour and halves another via 1-2-4). Deductions like these are the whole charm of Kropki — tiny facts with grid-wide consequences.
Solving Strategies
1. Start at the black dots
Three valid pairs means a black dot instantly reduces two cells to a handful of options. Two black dots in a row or column force a doubling chain: on six digits, a three-cell chain must be 1-2-4 in some order. Find the black dots, pencil their pairs, and the grid opens up from there.
2. Read the empty borders
Beginners solve the dots; strong solvers also solve the gaps. If a cell holds 3 and its neighbour shows no dot, that neighbour can't be 2 or 4 (consecutive) and can't be 6 (double) — three of five candidates gone from a blank border. On puzzles with no given digits, alternating between dot logic and no-dot logic is the entire solving loop.
3. Anchor with 1 and 6
The extremes have the fewest relationships: 6 is consecutive only with 5 and doubles only 3; 1 is consecutive only with 2 and halves only 2. Cells with many dots around them usually can't be 1 or 6, while isolated, dot-free cells often must be. Placing the extremes first mirrors the bread-first strategy of Mini Sandwich Sudoku — pin the rare digits, then fill the middle.
4. Finish with classic scanning
Dots narrow candidates, but rows, columns, and boxes place them. Every technique from classic Mini Sudoku — cross-hatching, naked singles, pairs — applies unchanged. The rhythm of a good Kropki solve is: dot deduction, box scan, dot deduction, box scan.
Tips for Beginners
- Write the pair tables down once. After a puzzle or two, 1-2 / 2-4 / 3-6 will be burned in permanently.
- Check every border of a solved cell. Each placed digit turns all its dots — and non-dots — into fresh eliminations for the neighbours.
- Expect empty starting grids. No givens doesn't mean no information; the dots are the givens.
- Use candidates freely. Auto pencil marks in Sudoku - Brain Puzzles keep the dot pairs visible so you can focus on the chain logic.
- Step up when ready. Full 9x9 Kropki adds one more black-dot pair (4-8) and longer chains — the jump is smaller than it looks.
Mini Kropki is arguably the best puzzle-per-minute value in the Sudoku family: a complete, self-contained logic system you can learn in five minutes and enjoy for years. Master the dots on the small grid, and the 9x9 version becomes a natural encore.