24

Mint

This is a Perl script to list "distinct" solutions to the 24 puzzle. The lists of solutions to each N puzzle are organized in the solutions directory and are licensed under CC0.

• Solutions to 24
• Solutions to 10

Bibliography

• auntyellow/24 (2017).
  • Solvers written in JavaScript and Java.
• Azuma, Seiichi (2014). "Expressions with n variables".
  • An algorithm for generating inequivalent expressions.
• Chang, Cheng (2012). 4nums.com.
  • A theory and a web service that returns distinct solutions to a.b.c.d = N, where 1 <= a, b, c, d <= 99 and 1 <= N <= 9999.
• Dominus, Mark Jason (2017). "Recognizing when two arithmetic expressions are essentially the same".
  • The Ezpr data structure and a solver written in Perl.
• Fan, Mei Hui (2022). mhfan/inrust.
  • Solvers written in Rust and C++.
• Yuuki (2018). "Ten puzzle" (in Japanese).
  • Remarks on the (super-)Catalan numbers.
• OEIS
  • Du, Zhao Hui (2008). A140606 (Number of inequivalent expressions involving n operands).
  • Radcliffe, David (2012). A182173 (allowing unary minus).
  • Azuma, Seiichi (2014). A247982 (ignoring sign).
  • Dushoff, Jonathan (2022). A351922 (allowing exponentiation).

History

[show]

• - 2013: Learned about the 10 puzzle (a variation popular in Japan).
• 2022-07: Realized that eliminating duplicate solutions could not be done with a CAS such as SymPy and started the research.
• 2022-09: Finished writing the script and failed to solve the 0 puzzle.
• 2023-01: Abandoned the research and archived the results on 24-puzzle-solver/24-puzzle-solver.
• 2024-02: Reorganized the results in this repo, essentially unchanged.