If a solution path of 100 moves can be broken down into, say, 10 sub tasks then the complexity of the problem is drastically reduced. break down the overall goal into sub tasks.If there are on average, say, 2 possibilities for each move and the solution takes 100 moves then a brute force search would require to search 2 100 paths to find the solution. The shortest solution might contain 100, 300 or even 1000 moves (our simplest game 1 already needs 73 moves, game 8 needs 126 moves). dead position: a position from which the solution can not be reached.solution path: the sequence of moves from the original position to the solution.solution: a position where each box is sitting on a dot.position: the whole problem with the worker and all boxes being at a certain place.move: one step of the worker whether pushing or not pushing a box.The following terms will be used throughout this guide:

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