Dominos One-by-One

0-4 0-3 0-2 0-1 0-0
1-4 1-3 1-2 1-1
2-4 2-3 2-2
3-4 3-3
  Into a 4x4 grid, place the 15 dominos in this manner:  Place one domino in the grid, one digit per square.  Place the second domino by overlapping the first by a matching square (the squares that overlap must have the same digit.)  Place each successive domino in the same way, overlapping one square and filling an empty square until all 16 squares are filled.

Extension: Is it possible to make this a magic square as well?

Source: Puzzle 09 from the 2003 Puzzle Design Tournament at

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