Also known as:
The Tatami grid is a square with sides of a variable length (between 6 and 15 squares) inside which are rectangles or Tatamis measuring 1x3, 1x4 or 1x5 squares each, placed side by side. These rectangles supposedly resemble Japanese flooring panels, hence the puzzle's name.
Like many other logic puzzles, Tatami is based on Euler's Latin square, but with an essential difference. Whilst the Latin square cannot have repeated numbers on each line and column, in Tatami the digits must be repeated in rows and columns, but never within a rectangle.
The puzzle has been promoted enthusiastically by Italian puzzle publisher nonzero, from whom the attached sample is provided.