Does the number of clues determine the difficulty of a Sudoku puzzle?
Some believe that the difficulty of a Sudoku puzzle depends solely on the number of initial clues, and is independent of the way the clues are arranged on the grid or the particular clues given. Below is an analysis of the variation in difficulty of the 17 clue puzzles. Were the difficulty to depend solely on the number of clues, all the 17 clue puzzles should have very similar ratings. I calculated the difficulty rating for the subset (40553) of the 47793 puzzles which can be solved using only the hint algorithms in SourGumdrop – i.e. without guessing. This was done twice. Once using the “provocative” standard algorithm scores I first posted several years ago, and which are used to calculate the scores for SourGumdrop’s built-in puzzles, and the second using the scores H1 = 1, H2 = 6,H3 = 6, L1 = 2, L2 = 2, N2 = 3, N3 = 3, N4 = 6, XW = 9, SF = 9, JF = 20, which probably more accurately reflect the difficulty of recognising and using each algorithm. The results are plotted in Figure 1.
