Imagine a 4-dimensional chess board, but with only 4 squares a side. So, $4\times4\times4\times4=256$ sub-hypercubes.
Your mission - should you choose to accept - is to:
Find a Knight's Tour
Four dimensional spaces are actually quite easy to visualize:
The orange squares represent the possible destinations of a knight that starts from the red square - it moves $1$ in a dimension and $2$ in another.
If the coordinates of a knight are $(x,y,z,t)$, then we can get to $(x\pm1,y\pm2,z,t)$ or $(x,y\pm1,z,t\pm2)$, or any other combination, as long as we remain on the board.
The coordinates of the knight shows are $(1,1,1,1)$, with depth representing the $z$-axis, and the $t$-axis being represented by the multiple grid show left to right.
Therefore the first few coordinates of the orange squares, read left-right, top-bottom, are:
$(3,1,0,1), (1,1,0,3), (1,3,0,1), (3,0,1,1), (1,0,1,3), (3,1,1,0), \dots$