Kropki Sudoku
2
1
4
5
7
4
9
8
2
1
7
4
2
7
3
8
4
6
3
1
4
9
8
1
2
3
7
3
5
6
7
4
2
7
6
4
9
1
Kesilapan
0/3
Skor
-
Masa
00:00
Kemajuan0%
Mudah ยท Sudoku Kropki
Tukar kesukaran di atas โ
Cara bermain Kropki Sudoku
Peraturan Sudoku standard terpakai. Titik hitam antara dua sel bersebelahan: satu digit adalah tepat dua kali ganda yang lain. Titik putih: dua digit adalah berturutan (beza 1). Tiada titik: tiada syarat yang terpakai.
Panduan penuh โ
Titik putih = digit berturutan; titik hitam = satu digit adalah dua kali ganda digit yang lain
Kropki Sudoku Mudah
Kropki Sudoku Sederhana
Kropki Sudoku Sukar
Kropki Sudoku Pakar
Apakah Kropki Sudoku?
Kropki Sudoku meletakkan titik antara pasangan sel bersebelahan. Titik putih bermaksud dua digit berbeza tepat 1 (berturutan). Titik hitam bermaksud satu digit adalah tepat dua kali ganda yang lain (contohnya, 2 dan 4, atau 3 dan 6). Di mana tiada titik muncul, kedua-dua keadaan tidak terpakai. Sesetengah teka-teki Kropki menggunakan 'kekangan negatif' di mana ketiadaan titik menjamin kedua-dua keadaan tidak berlaku, memberikan lebih banyak maklumat.
Sekilas Pandang
| Jenis kekangan | Hubungan Petak |
| Biasa diberi | 18โ24 |
| Penilaian kesukaran | โ โ โ โโ 3/5 |
| Purata masa selesaikan โ Mudah | 8 min |
| Purata masa selesaikan โ Sederhana | 18 min |
| Purata masa selesaikan โ Sukar | 35 min |
| Purata masa selesaikan โ Pakar | 62 min |
Cara Menyelesaikan Kropki Sudoku
| Teknik | Apa yang dilakukannya | Tahap |
|---|---|---|
| White Dot Pairs | White dots mark consecutive digit pairs: (1,2), (2,3), โฆ, (8,9). Cross-reference with row and column constraints. | Lanjutan |
| Black Dot Pairs | Black dots mark double-relationship pairs: (1,2), (2,4), (3,6), (4,8). Only these four combinations are valid. | Lanjutan |
| Negative Constraint | No dot between two cells means they are neither consecutive nor in a 1:2 ratio โ a powerful elimination on every unmarked adjacent pair. | Lanjutan |
| Dot Chain Analysis | A sequence of connected dots forms a digit-value chain. Enumerate valid digit sequences for the entire chain simultaneously. | Lanjutan |
| 1-2-4 and 2-4-8 Chains | A black dot adjacent to a white dot often forces the common 1โ2โ4 or 2โ4โ8 chain. | Lanjutan |
Purata Masa Selesaikan
Mudah
8 min
Sederhana
18 min
Sukar
35 min
Pakar
62 min
Soalan Lazim
Apakah Kropki Sudoku?
Kropki Sudoku is a variant where dots appear between adjacent cells. A black dot means one of the two cells holds exactly double the value of the other. A white dot means the two cells hold consecutive digits (differing by 1). Standard Sudoku rules apply, and crucially: if there is no dot between two adjacent cells, they are guaranteed NOT to be consecutive and NOT to have a double relationship.
What does a black dot mean?
A black dot between two cells means one digit is exactly twice the other. For example: 1&2, 2&4, 3&6, 4&8. Note that 1&2 satisfies both black (1ร2=2) and white (|2-1|=1) conditions โ in Kropki Sudoku, a black dot is used when only the doubling relationship holds, not the consecutive one, unless specified otherwise.
What does a white dot mean?
A white dot between two cells means the digits differ by exactly 1: they are consecutive. Valid pairs are 1&2, 2&3, 3&4, 4&5, 5&6, 6&7, 7&8, 8&9. The order doesn't matter โ either cell can hold the higher or lower digit.
How does the no-dot constraint work?
In standard Kropki Sudoku, every possible black dot and white dot relationship is marked. This means that if no dot appears between two adjacent cells, you can be certain those cells are neither consecutive nor in a 1:2 ratio. This negative information is just as powerful as the positive dot clues.
Is Kropki Sudoku harder than regular Sudoku?
Easy Kropki puzzles are accessible and make excellent teaching tools for the variant. Hard and expert puzzles are significantly more challenging than classic Sudoku because you must simultaneously track dot relationships and the negative no-dot constraint across every pair of adjacent cells.
How long does Kropki Sudoku take to solve?
Easy puzzles take 8โ18 minutes. Medium puzzles run 18โ35 minutes. Hard puzzles average 35โ65 minutes and expert puzzles often exceed 90 minutes. Mastering the no-dot constraint is the key to faster solve times at all levels.