N-Queens Solver

This project provides a flexible, efficient, and dynamically optimized solution to the N-Queens problem. It includes multiple solving methods, each tailored for different board sizes, ensuring the best performance for any n.

Available as a Ruby gem at https://rubygems.org/gems/n_queens

• Ruby Gem API: Clean public API via NQueens::Solver
• Dynamic Method Selection: Automatically selects the most efficient algorithm based on the board size (n)
• Backtracking with Pruning: Optimized backtracking algorithm for small board sizes (n <= 10)
• Parallel Bitmasking: Utilizes multi-core CPUs to solve large board sizes efficiently (n 11-17)
• Parallel Bitmasking to File: Writes solutions to disk for very large board sizes (n >= 18)
• OEIS A000170 Ground Truth: NQueens::KNOWN_COUNTS provides peer-reviewed solution counts for n=1..15
• Execution Time Reporting: Displays the method used, the number of solutions, and the total execution time

gem install n_queens

Or add to your Gemfile:

gem "n_queens", "~> 1.0"

git clone https://github.com/unixneo/n_queens.git
cd n_queens
bundle install

require "n_queens"

# Solve for a given board size
result = NQueens::Solver.new(8).solve

result.count      # => 92
result.solutions  # => Array of 92 placement arrays (nil for n >= 18)
result.method     # => :backtracking or :parallel_bitmask
result.duration   # => Float elapsed seconds

# Each solution is an array of column positions indexed by row
# result.solutions[0] => [0, 4, 7, 5, 2, 6, 1, 3]
# meaning: queen in row 0 is at column 0, row 1 at column 4, etc.

# OEIS A000170 ground truth solution counts
NQueens::KNOWN_COUNTS[1]  # => 1
NQueens::KNOWN_COUNTS[4]  # => 2
NQueens::KNOWN_COUNTS[8]  # => 92
NQueens::KNOWN_COUNTS[12] # => 14200
NQueens::KNOWN_COUNTS[14] # => 365596

# Version
NQueens::VERSION  # => "1.0.0"

# Default (8 Queens)
ruby n_queens.rb

# Custom board size
ruby n_queens.rb 12

bundle exec rspec

Expected output:

7 examples, 0 failures

gem build n_queens.gemspec
gem push n_queens-1.0.0.gem

2026-04-23 >>> Started Solving N-Queens with 8 Queens using Backtracking with Pruning Method
2026-04-23 >>> Number of solutions: 92 for 8 Queens in 0.012345 seconds

This project is licensed under the MIT License. See the LICENSE file for details.

• Wikipedia: 8 Queens Problem
• OEIS A000170
• RubyGems: n_queens

• unixneo (Tim B.) - PI
• Claude (Anthropic) - Gemspec Architect
• Codex (OpenAI) - Coder