The following numberphile video has me stumped.
Why is this Puzzle Impossible? - Numberphile
It describes the use of parity in permutations to show that the following sequence is impossible
{15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, blank}
because the parity of moves required is odd, and only even parity moves are achievable in the 15 puzzle.
However the following sequence does have even parity and therefore should be achievable.
{15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, blank, 1}
From the puzzle's perspective it is trivial to go from this sequence to the impossible solution which is a contradiction. What is the error in this logic ?