The methods that fall into the "Medium" category are Naked Quads, Hidden Quads
and Intersection Removal. Although the quads are just an extension of the pairs and triples, they are quite rare.
Out of all boards, the Naked Quads method constitutes only 0.1% of all methods and the Hidden Quads only 0.04% of all methods.
In comparison, Intersection Removal constitutes 24% of all methods, which makes it among the most commonly used methods in solving Sudoku (second to Naked Pairs at 25%). If you are stuck on a sudoku board, better watch out for an Intersection Removal somewhere.
A medium board contains all previously mentioned methods in addition to the new ones. We make sure that there are some "Easy" methods and more "Medium" ones, so that user can have a bit more challenge when playing. Medium boards are the most rare ones in our set of 200, 000 boards as very often, boards which are more complicated will use one of the more advanced strategies.
All methods up to and including medium can be regarded as "simply by logic". Most casual sudoku players will be solving sudoku boards by using these basic methods. Thus, most newspapers and sudoku games will not generate harder boards, just because the majority of players will not be able to solve them. For example, on most sudoku games in the app stores, a "Very Hard" sudoku will often be graded as a "Medium" board in our Board Generation.
If you would like to extend your knowledge and become a sudoku master, we suggest moving on to the next categories, which include "colouring" and "wing" strategies, among others. Without guessing, it will be very difficult to solve harder boards, otherwise.