How To Solve Tatami Puzzles
The puzzle consists of a square grid covered with rectangular mats, each one being from 1 to N in length, where N is the number of spaces in the mat for that puzzle. Place numbers from 1 to N into the puzzle cells. The numbers within a mat must all be different. Horizontally or vertically adjacent cells must not contain the same number. Each row and column of the puzzle must have the same number of appearances of each number.
Here is a typical Tatami puzzle grid. The grid size can be smaller or larger and varies in difficulty.
The grid contains several same-sized mats; in this case, each is four spaces long, running vertically and horizontally. All mats are only one space wide.
Each space requires a single number from 1 to 4. Some numbers are provided in the puzzle already.
Each mat must have all the numbers from 1 to 4. There cannot be duplicate numbers in a mat.
So far seems easy. Here's the twist!
Horizontally or vertically adjacent cells must not contain the same number.
Each row and column of the puzzle must have the same number of appearances of each number. So if in the first column you have three 4s, then every row and column can only have three.
The solution to the puzzle is shown here.
Notice that every mat contains numbers from 1 to 4 with no duplicates. Each number appears an equal number of times in each row and column. None of the adjacent numbers are the same.