CS194 Project: Sudoku Difficulty

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CS194 ProjectSudoku Difficulty

• Kha Chu
• Advisor Professor Sahai

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The Problem

• Sudoku puzzle difficulties tend to not match the
  actual observed difficulty.
• Estimations of difficulty tend to stem from
  number of numbers revealed from the start.
• Problem such a method is innacurate, as a puzzle
  with many numbers revealed may be impossible to
  solve without guessing.

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How to Fix the Problem

• For a given puzzle, difficulty should not stem
  from how much is revealed, but how often highly
  logical analysis is used to solve the puzzle.
• To write a program to do such a thing, it is
  needed to analyze the many techniques used to
  solve a puzzle.
• Current sudoku solvers have an array of a bunch
  of cells and remove numbers from them through
  using rules, my algorithm seeks to be closer to
  how humans solve them.
• My algorithm will be based off of how I solve
  puzzles.

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Outline

• Cycle through numbers and each block (a set of
  3x3 cells of the 9x9 puzzle).
• For each block for each number, determine which
  cells the number cant be in (like by looking at
  the placement of the number in other blocks), and
  if theres only one possible number, place the
  number in there.
• A number can be determined through indirection
  if the row or column of a cell can be determined,
  and two of the cells are cancelled, the placement
  of the number is found.
• Once a cycle through the numbers produces no
  changes, proceed to other methods.

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Other Methods of Solving

• Check each row, column, or block for missing
  numbers, if there is just one missing, fill it
  in.
• If there is a choice between two numbers in a
  series of blocks, guess one and proceed until
  done, or until a contradiction is found, then
  test the other.
• Technique Difficulty Ranking
• One open cell left in a row, cell, or block 0
• Indirect determination 1
• Guessing 2

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Indirect Determination

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Plan

• First quarter Create the solver that will solve
  a sudoku puzzle with the tools given.
• Second quarter Use the solver in conjunction
  with random number placement to create a puzzle
  generator that yields a puzzle with a unique
  solution. Generate a variety of puzzles and
  survey various peoples opinions on the
  difficulty of the puzzles. Find the correlation
  between generated difficulty and perceived
  difficulty.
• Third quarter Using the results from the survey,
  tweak the generator and solver in order to
  increase correlation between generated and
  perceived difficulty.