The library of logic contains a set of example problems that can be used to train LLMs to think logically

Each example in the library is a simple problem/game that is easy for a human or a computer algorithm to solve, but hard for LLMs (currently) to solve

Some examples include, Sudoku and tic tac toe

Each example in the library of logic contains 3 things:

1. A short description describing the format of the problem and the rules
2. A computer program that taking a input in the correct format can

• compute the "next step"
• or produce an error if an invalid step has been taken
• optionally an explanation of why that step was taken (or invalid)

3. some example problems, or a problem generation program

The goal of this library is ultimately to be able to produce a dataset of the following form:

User
Please solve this problem:
{ rules and format}
{example problem}
Assistant: 
Certainly, I will work step-by-step.  Here is first step:
{output of the first step of the computer program}
User:
Good, keep going
Assistant:
Here is the next step
{output of the next step of the computer program}
...

Here is a list of problems that hypothetically would fit well in the library of logic

• Playing Chess
• Solving Sudoku
• Solving a Maze
• Planning a Multi-Stop Trip
• Tower of Hanoi
• Eight Queens Puzzle
• N-Queens Problem
• Solving Crossword Puzzles
• Peg Solitaire
• Playing Checkers
• Tic-Tac-Toe
• Minesweeper
• Playing Connect-4
• Magic Square
• Knights Tour
• Rat in a Maze
• Word Search
• Coin Change Problem
• Sum of Subsets
• Playing Mastermind
• Travelling Salesman Problem
• Playing Reversi
• Sorting a Hand of Playing Cards
• Marble Solitaire
• Chinese Checkers
• Chutes and Ladders
• Balderdash
• Jigsaw Puzzle Solving
• Cryptarithmetic Puzzles
• Palindromes Detection
• Determining Leap Years
• Counting Number of Islands
• Coloring a Map
• Playing Cribbage
• Finding Prime Numbers
• Bingo Game
• Nim Game
• Playing Spades
• Hidden Picture Puzzle
• Counting Money Change
• Matching Brackets
• Solving Paint-by-Numbers
• Solving Kakuro
• Finding Waldo
• Playing Pinochle
• Finding Eulerian Path
• Playing Whist
• Playing Old Maid
• Solving Word Ladder Puzzles
• Playing Rummy
• Solving Futoshiki
• Playing Hearts
• Making a Rhyme
• Playing Bridge
• Playing Crazy Eights
• Identifying Palindrome Sentences
• Calculating Area of Irregular Shapes
• Identifying Anagrams
• Solving Nonograms
• Detecting Cycle in a Directed Graph
• Playing Uno
• Playing Snap
• Calculating Tips
• 1D Cellular Automata
• Long multiplication
• Long Division
• Long Polynomial Division
• parity (compute the parity of a a binary sequence of arbitrary length)
• copy (copy a sequence, repeating each symbol k times)
• addition (arbitrary length)
• balanced parenthesis