Is Dominosa NP-Hard?

Question

Dominosa is a relatively new puzzle game. It is played on an $(n+1)\times(n+2)$ grid. Before the game begins, the domino bones $\left(0,0\right),\left(0,1\right),\ldots,\left(n,n\right)$ are placed on the grid (constituting a perfect tiling). In the next step, the domino bones are hidden, leaving only the numbers revealed. The purpose of the game is to recover the original arrangement of the domino bones. You can play the game here: http://www.puzzle-dominosa.com/:

Rules:

The rules are simple. You have to find the location of all the dominoes on the grid. A domino is a pair of numbers. You can only have one of each pair.

I have some polynomial algorithms that solve a relatively small part of the puzzle. I could also show that typical Dominosa grids have at least $2^{\frac{n}{2}+o\left(n\right)}$ solutions.

Is Dominosa NP-Hard?