However, if you examine the arrangement which was being sold by Loyd, in which the 14 and 15 were swapped, then the value of the disorder parameter is one, Dp = 1, i.e. the only pair of tiles out of order are the 14 and 15. For Loyd’s arrangement the disorder parameter has an odd value! Yet we know that any arrangement derived from the correct arrangement has an even value for the disorder parameter. The conclusion is that Loyd’s arrangement cannot be derived from the correct arrangement, and conversely it is impossible to get from Loyd’s arrangement back to the correct one – Loyd’s $1,000 was
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