Pack 28 dominos into an 8x8 square so that none of them can slide.  Then make it a magic square.  A solution:

Wei-Hwa Huang, Juha Saukkola, Gareth Rees, and Joseph DeVincentis sent solutions.  The solution in the image above is by Jukka-Pekka Ikaheimonen.

This write-up below by Gareth Rees.  A similar write-up is at the website of  Torsten Sillke.
The 28 dominoes can cover 56 squares of the chessboard, leaving 8
"holes".  I will focus on the positions of these holes.

No two holes can be adjacent orthogonally or diagonally, because there's
no way to put dominoes in the adjacent squares, so all adjacent squares
must be holes too; hence holes cover the whole board.

I can't put a hole (represented by "O") at a corner, because   Oa......
in the diagram at the right the domino a is forced, but then   ba......
there's no way to cover square b.        ........

I can't put a hole on an edge, because dominoes a and b in     ..aOb...
the diagram at the right are forced, and then there's no way   ..acb...
to cover square c.        ........

I can't place two holes with only one square between them      ........
because in the diagram at the right, after placing piece a     .bbagf..
(WLOG) pieces b, c, d, e and f are forced, and then there's    .cOaOf..
no way to cover sqaure g.        .cddee..

I can't place three holes in the configuration at the right    ........
because I must cover the squares marked "a" with dominoes      ..aOa...
aligned vertically, and then there's no way to cover the       .OabaO..
square marked "b".        ........

I believe (but cannot prove other than by exhaustive search) that the
above five conditions are sufficient to ensure that the only possible
arrangements of the 8 holes are

........
.O....O.
....O...
..O.....
.....O..
...O....
.O....O.
........

and its reflection.  The arrangement of dominoes is then forced to be:

ccbrrhhg
d bqqe g
daay eff
xw yzzst
xwBBA st
nnm Aiil
o muuj l
oppvvjkk

(The order of the letters - lowercase then uppercase - gives one forcing
sequence.)

--
Gareth Rees