Tatamidoku is a fun game/logic puzzle I found via Andrea Sabbatini's 100 Logic Games, though it is just named "Tatami" there. This is not the same as Tatamibari.

Unfortunately, the hint system in 100 Logic Games is not ideal, simply providing the answer for the topmost leftmost square. Instead, I decided to build a generator and algorithmic solver, in order to provide more gentle hints (e.g. "look at this column") and to create my own puzzles.

Tatamidoku is played on a square grid, which is also divided into sections, a little like sudoku. However in Tatamidoku, the subdivisions are rectangular and just a single cell wide or tall. Each section contains the same number of cells, and the grid is at least two sections across. Common sizes are 3-, 4-, or 5-cell sections, and 2- or 3-section grids.

This layout can produce an effect rather like tatami mats used for flooring in traditional Japan, hence the name.

To be able to more easily explain the rest of the rules, let's assume that each section has n cells, and the grid is s sections across, for a total of g = n × s cells on each side.

The grid must be filled using the digits from 1 to n. Similar to sudoku, each section must contain each digit exactly once. In addition to this, each row and column must contain each digit s times and cells that share a border must not have the same digit (though it's permitted diagonally).

One of the most common layouts is 3-cell sections and 6x6 (i.e. 2-section) grids. These sections must be filled with the digits 1, 2, and 3. Each of those digits must appear twice in every row and every column, and orthogonally adjacent cells must have different values.

For example, this completed grid:

┏━━━┳━━━┳━━━┳━━━┯━━━┯━━━┓
┃ 1 ┃ 2 ┃ 3 ┃ 2 │ 3 │ 1 ┃
┠───╂───╂───╊━━━┿━━━┿━━━┫
┃ 3 ┃ 1 ┃ 2 ┃ 1 │ 2 │ 3 ┃
┠───╂───╂───╊━━━┿━━━┿━━━┫
┃ 2 ┃ 3 ┃ 1 ┃ 3 │ 1 │ 2 ┃
┣━━━╋━━━╇━━━╇━━━╈━━━╈━━━┫
┃ 3 ┃ 2 │ 3 │ 1 ┃ 2 ┃ 1 ┃
┠───╊━━━┿━━━┿━━━╉───╂───┨
┃ 2 ┃ 1 │ 2 │ 3 ┃ 1 ┃ 3 ┃
┠───╊━━━┿━━━┿━━━╉───╂───┨
┃ 1 ┃ 3 │ 1 │ 2 ┃ 3 ┃ 2 ┃
┗━━━┻━━━┷━━━┷━━━┻━━━┻━━━┛

Notice how the sections don't necessarily align, possibly made clearer by highlighting them with their direction:

┏━━━┳━━━┳━━━┳━━━┯━━━┯━━━┓
┃ | ┃ | ┃ | ┃ - │ - │ - ┃
┠───╂───╂───╊━━━┿━━━┿━━━┫
┃ | ┃ | ┃ | ┃ - │ - │ - ┃
┠───╂───╂───╊━━━┿━━━┿━━━┫
┃ | ┃ | ┃ | ┃ - │ - │ - ┃
┣━━━╋━━━╇━━━╇━━━╈━━━╈━━━┫
┃ | ┃ - │ - │ - ┃ | ┃ | ┃
┠───╊━━━┿━━━┿━━━╉───╂───┨
┃ | ┃ - │ - │ - ┃ | ┃ | ┃
┠───╊━━━┿━━━┿━━━╉───╂───┨
┃ | ┃ - │ - │ - ┃ | ┃ | ┃
┗━━━┻━━━┷━━━┷━━━┻━━━┻━━━┛