Here are 20 pages of REALLY HARD SUDOKU PUZZLES in 2 volumes.
They are difficult, but fair. At each step of the solution there is at least 1 square that clearly must contain a specific number.
Here's how these puzzles were generated: Thousands of solutions puzzles were generated. From each solution puzzle, up to 1000 puzzles were created by removing squares until there were 24 or less squares with numbers in them, all of them solvable in a "human" way. The software then solved each of these puzzles 100 times in a "human" fashion, and at each step examined how many squares could be filled in a straightforward way.
A "straightforward way" means that a square either has only 1 number that could be placed in it and keep the puzzle legal, or that by examining a row, column, or 3x3 box you could determine that only a single number can be placed in a specific square of the row, column or box.
For each step of the solution, the software counted the number of squares that could be filled in this way. The puzzle with the lowest average number of squares that can be solved at any step was rated the most difficult. These 80 puzzles were the most difficult: at times there will be only a single square that can be solved simply.
Good luck. If you get really stuck and want a hint, send an email to admin@4puz.com with the partial solution you have.
