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A solution is optimal if the sequence of moves is as short as possible. The highest value of this, among all initial configurations, is known as God's number, [3] or, more formally, the minimax value. [4] God's algorithm, then, for a given puzzle, is an algorithm that solves the puzzle and produces only optimal solutions.
By a result of Raphael M. Robinson this is again solvable whenever d = d 1 × d 2 for two numbers d 1 and d 2 such that the d 1 - and d 2-dimensional cases are themselves solvable. For instance, according to this result, it is solvable for dimensions 4, 6, 8, 9, and other 3-smooth numbers. In all dimensions, the inequality of arithmetic and ...
The Slothouber–Graatsma puzzle is a packing problem that calls for packing six 1 × 2 × 2 blocks and three 1 × 1 × 1 blocks into a 3 × 3 × 3 box. The solution to this puzzle is unique (up to mirror reflections and rotations). It was named after its inventors Jan Slothouber and William Graatsma. The puzzle is essentially the same if the ...
[1] The puzzle is known to have appeared as early as 1981, in the book Super Strategies For Puzzles and Games. In this version of the puzzle, A, B, C and D take 5, 10, 20, and 25 minutes, respectively, to cross, and the time limit is 60 minutes. [6] [7] In all these variations, the structure and solution of the puzzle remain the same.
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An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly at a constant rate of 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc.
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Ignoring the order in which the cubes are stacked, the total possible number of arrangements is therefore 3,456 (24 * 24 * 24 * 24 / (4 * 4!)). The puzzle is studied by D. E. Knuth in an article on estimating the running time of exhaustive search procedures with backtracking. [2] Every position of the puzzle can be solved in eight moves or less ...