4x4 slide puzzle

A 44 slide puzzle (also known as a 15-puzzle) is a sliding puzzle that consists of a 44 grid with 15 numbered square tiles and one empty space. The goal is to rearrange the tiles from a scrambled initial state into numerical order (1 to 15, left to right, top to bottom) by sliding them into the empty space. How to Solve a 44 Slide Puzzle: Understand the Rules: - You can only move tiles adjacent to the empty space (up, down, left, or right). - Diagonal moves are not allowed. Basic Solving Strategy: - Solve the Top Row (1-4): - Move tiles 1, 2, 3, and 4 into their correct positions one by one. - Avoid disturbing already placed tiles. - Solve the Second Row (5-8): - Repeat the process for the second row. - Solve the Third Row (9-12): - Continue similarly. - Solve the Last Row (13-15): - The last row is trickier because you have limited space. - Use sequences like "corner rotation" (e.g., 13-14-15) to arrange them correctly. Advanced Techniques: - "Snake" Method: Move tiles in a sequential path (123481215141395671110). - "Empty Space" Management: Always keep track of where the empty space is to avoid blocking key tiles. Avoiding Unsolvable Cases: - Some initial configurations are unsolvable due to parity (mathematical property). - If the puzzle seems stuck, check if the starting scramble was valid (requires an even number of swaps to solve). Example: Solution Steps: Move 15 left to fill the empty space. Swap 14 and 15 to fix the order. Tips for Faster Solving: Practice smaller puzzles (33) first. Plan ahead to avoid unnecessary moves. Use algorithms for the last few tiles (e.g., "3-cycle" method). Would you like help with a specific puzzle configuration?