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a 31-step expansion path for a 17c puzzle
(1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1 1 2 5 6)

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interesting to see the first 24 1-expands are their own BRT-expands.
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the algorithm builds several expansion paths simultaneously and for each of them among the 1brt possible for the next step chooses the one(s) with the smallest number of values
for this puzzle i made three attempts, the first with a sample of 1000 paths at each step and i obtained an expansion path of 28 steps (1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 1 13), then with a sample of 3000 paths and i obtained this expansion path of 31 steps, and finally with a sample of 5000 paths and i obtained an expansion path of 29 steps (1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 1 13)
31 steps may not be the longest expansion path for this puzzle, but it is impossible for me to be exhaustive, and a larger sample size does not guarantee a longer expansion path