Renban Sudoku Rules: What Renban Lines Mean in Sudoku

Renban Sudoku is a Sudoku variant where another constraint or rule is added in addition to the regular rules of Sudoku. 

This is done by creating certain Renban regions by either adding lines to the grid (known as Renban lines) or shading cells a different color. Such as in the example below. 

The additional rule is that these adjacent cells contain a set of distinct consecutive digits.

The digits, however, can appear in any order as long as they as a set are consecutive.

So, for example, 2-5-3-4 would be an acceptable sequence of digits in a Renban line or region as the four digits are consecutive even though they do not appear in order. 

Another important Renban rule is that the digits cannot repeat on the line or region. Even if allowed by the regular rules of Sudoku (that every row, column, and 3×3 region contains the numbers 1 through 9 exactly once each). 

Make sure you also do not mistake thermometers in Thermo Sudoku or arrows in Arrow Sudoku for Renban lines.

Renban Sudoku tips

This simple additional constraint gives rise to some lovely logic that you can apply to solve the puzzles. 

For example, if you take a look at the bottom right Renban in the example above, you’ll notice it already contains the digits 2 and 3. And because it’s only four-cells and the two remaining digits must form a consecutive set with the 2 and 3, there are only two possibilities for what the four digits can be:

• 1-2-3-4
• 2-3-4-5

However, if you look carefully you’ll also notice that there’s already a 1 in the same 3×3 region as the two empty cells in the Renban. 

This means that we now know that these two emply cells must be a 4 and 5 as 1 has been eliminated as a possibility. 

But remember that we do not immediately know which order they appear in as the digits do not have to ordered consecutively (they can appear in any order).

Solution to the example