This puzzle is Copyright © 2007 by James Dow Allen

Dominoes Puzzle #2

Only possible (2-2)'s involve 2*. Only possible (4-4)'s involve 4*. (0*-1) at center-left is impossible -- it would force (0-5) below it, and then a duplicate (0-1).

With (5,4*) forbidden, the only possible (5-4)'s involve 5*.

The only places for (2-1) and (2-6) involve the two 2! cells, so (2!-3) is ruled out. This means (3*-1) isn't a domino -- it would lead to a duplicate (3-1) right next to it.

Each of the 4! cells can connect only to a 2 or a 1; this rules out other possible locations for (4-2) or (4-1). By now we've located our first certain domino: a (6-4) near upper left.
 
 

0 6 3 5 2 4 1 2 3 6 6 6 5 2 5 6 2 4 1 5 6 0 1* 1 0 1 0 5 3 3 3 3 0 1* 4 4 4 6* 6* 2 5 5 5 0 3 4 3 1 0 1* 4 0 2 2 2 4

With (6-4) forced, other (6-4) locations become impossible.

Each of the three 1* can connect only to 0, 1, or 5, so other locations for (1-0), (1-1) and (1-5) become impossible. By now, adjacent to the (6-4) domino, a (6-1) and (1-1) domino are each seen to have become forced.

This forces the (0*,0*) nextdoor to the (1-1) to be a domino -- otherwise there would be an odd-sized isolated group in the lower right.

Finally, only the site (6*,6*) is left for the (6-6) domino.
 
 

0 6 3 5 2 4* 1* 2* 3 6 6 6 5 2 5 6* 2 4 1 5 6* 0 1 1* 0 1 0 5 3* 3 3 3* 0 1 4 4 4 6 6 2 5 5 5 0 3 4 3 1 0 1 4 0 2 2 2 4

After the obvious forces are made, we find that the (3-1), (4-1), (6-2), and (6-3) dominoes can each only be placed in a single site (shown with *).

These lead to straightforward forces, after which (2-0), (3-0), (4-0), (2-1), and (5-5) will all be single-site dominoes. After this, complete solution follows.
 
 

Dominoes Puzzle #2 -- Final solution

After applying previous forces, the (5-5), (3-3)
 
 

This puzzle is Copyright © 2007 by James Dow Allen