How to rate difficulty? Part 1: EASY puzzles

Nick70

We all agree that the easy puzzle are the ones where each move is a single candidate in a cell or a unit.

But how easy is easy? There surely are different levels of difficulty for problems only requiring the simplest of the rules.

I don't think there is an undisputable answer to this question, because difficulty is a subjective thing and it depends on several factors, some of which are systemic (solving method used: paper or computer, with pencilmarks or without, and so on), others are random (when there are multiple moves available, the one done first might affect the difficulty of subsequent moves).

The different kinds of single candidate moves are at the same level for a computer using the dancing links algorithm, but they are different for a human solver. When playing without pencilmarks, I find the "single candidate in box" rule to be the easiest. With pencilmarks, however, the "single candidate in cell" rule is obviously easier; especially if the pencilmarks are maintained by a program like Simple Sudoku Smile

Since I'm anyway interested in difficult puzzles that are very difficult to solve without some kind of computer assistance, I've decided to assume the puzzles are played with Simple Sudoku. Therefore, the player can always see perfect pencilmarks, and has the ability to filter them.

I figure that a player would load the sudoku, look for single candidates in cells, place them, and when there are no more filter the 1's, 2's and so on looking for single candidates in box/row/column.
Something that often happens is that while you have filtered one number, you can place it in a few cells one after the other. I assume that the player will always do that when possible, instead of continuously changing the filter.

When using filters, I consider a single candidate in a box to be easier to see than a single candidate in a row or column, because the nine cells are all contentrated in one place.

Finally, there is one point in the solution of a sudoku where the completion becomes trivial: you just have to fill in single candidates in cells until the end.

So, the parameters I have identified to rate the difficulty of an easy puzzle are:

1/ number of times the only single candidates are in a row or column (not in box or cell)
2/ number of times the filter on pencilmarks has to change
3/ number of cells to fill before reaching the point of trivial completion.

Things I haven't considered are the number of hints at the beginning, and the number of different moves available at any given point. Do you think they are important?

Here are a few puzzles supposedly in increasing order of difficulty. DO you agree with the rating?

Puzzle 1:
row/col moves: 0 filter changes: 0 triviality start: 0