Renzoku
Consecutive numbers, dot by dot
Renzoku is a number placement puzzle that combines Latin square rules with consecutive-number constraints. Fill an NxN grid so each row and column contains 1 through N exactly once. Dots between cells indicate those cells contain consecutive numbers (like 3 and 4). Crucially, the absence of a dot means the cells are NOT consecutive. This "negative information" from missing dots is just as important as the positive information from present dots, creating a unique two-way deduction logic.
How to Play Renzoku
Latin Square
Fill each row and column with numbers 1 through N exactly once (same as Sudoku without the boxes).
Dots = Consecutive
A dot between two cells means they contain consecutive numbers (differing by exactly 1, like 2 and 3).
No Dot = Not Consecutive
If there is no dot between two cells, their values must NOT be consecutive. This is critical information.
Both Directions
Dots appear on horizontal and vertical borders between cells. Check all four sides of each cell.
Given Numbers
Some cells start with numbers pre-filled to anchor your deductions.
All Information Given
Every consecutive pair has a dot, and every non-consecutive pair has no dot. You can trust both presence and absence of dots.
Strategy & Solving Tips
Renzoku is special because missing dots are as informative as present dots. Use both types of information aggressively.
- The number 1 can only be consecutive with 2, and N can only be consecutive with N-1 — dots next to these extremes are very constraining
- If a cell has no dots on any side, its value cannot be consecutive with any neighbor — this severely limits its options
- A chain of dots (A-B-C all connected by dots) means those cells form a consecutive sequence like 2-3-4
- No-dot constraints eliminate candidate pairs: if cell A has no dot with cell B, they can't hold values like (3,4) or (5,6)
- Combine dot/no-dot information with row and column uniqueness to narrow candidates quickly
- In a 5x5 grid, a cell with 4 dots on its borders must see the values 1-2-3-4-5 spread across itself and neighbors in a specific pattern
Renzoku FAQ
What does "Renzoku" mean?
Renzoku is Japanese for "consecutive" or "continuous," directly referring to the puzzle's core mechanic of identifying consecutive number pairs via dots.
Is the absence of a dot always meaningful?
Yes! This is what makes Renzoku unique. Every missing dot is deliberate and tells you those cells are NOT consecutive. This negative information is essential for solving.
How is this different from Futoshiki?
Both are Latin square puzzles with extra clues between cells, but the constraints are different. Futoshiki uses greater/less-than inequalities; Renzoku uses consecutive/not-consecutive dots. The reasoning patterns are quite distinct.
Can two consecutive cells both lack a dot with a third cell?
Yes. If cells contain 3 and 4 (consecutive, so they have a dot), both might not be consecutive with a neighboring cell containing 7 (no dots with either).
Ready to Play Renzoku?
Experience the unique two-way logic of Renzoku — where dots reveal neighbors and silence speaks just as loudly. Every piece of information, present or absent, leads to the solution.