Sixteen Numbers


You are going to place all numbers from 1 to 16 on a 4x4 chessboard such that all consecutive number pairs (1-2, 2-3, ..., 15-16) will be on the neighboring cells (left-right-top-down).

In how many different ways can this be done?

If the question was asked for a 2x2 chessboard, the answer would be 8.