6. Consider the heuristic function for the 8-puzzle given by: h(s) = sum of permutation inversions....

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6. Consider the heuristic function for the 8-puzzle given by: h(s) = sum of permutation inversions. For example, h(N) = 4+6+3+1+0+2+0+0 = 16 (there are 4 numbers smaller than 5 that come after 5, 6 numbers smaller than 8 that come after 8, and so on) for the following board configuration N: 5 8 421 3 6 STATE(N) Is h admissible? Justify your answer with a proof or counterexample. 7 6. Consider the heuristic function for the 8-puzzle given by: h(s) = sum of permutation inversions. For example, h(N) = 4+6+3+1+0+2+0+0 = 16 (there are 4 numbers smaller than 5 that come after 5, 6 numbers smaller than 8 that come after 8, and so on) for the following board configuration N: 5 8 421 3 6 STATE(N) Is h admissible? Justify your answer with a proof or counterexample. 7

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