+-------------+   ---------------------------------------------------
   | 16  3  2 13 |   The 23 magic "34 sums"
   |  5 10 11  8 |   of Albrecht Dürer's magic square will emerge
   |  9  6  7 12 |   by applying appropriate masks with 4 holes:
   |  4 15 14  1 |   4 + 4 + 2 + 4 + (1 + 1 + 1) + 2 + 4 = 23
   +-------------+   ---------------------------------------------------


4 rows:
   +-------------+   +-------------+   +-------------+   +-------------+
   | 16  3  2 13 |   |  .  .  .  . |   |  .  .  .  . |   |  .  .  .  . |
   |  .  .  .  . |   |  5 10 11  8 |   |  .  .  .  . |   |  .  .  .  . |
   |  .  .  .  . |   |  .  .  .  . |   |  9  6  7 12 |   |  .  .  .  . |
   |  .  .  .  . |   |  .  .  .  . |   |  .  .  .  . |   |  4 15 14  1 |
   +-------------+   +-------------+   +-------------+   +-------------+

4 columns:
   +-------------+   +-------------+   +-------------+   +-------------+
   | 16  .  .  . |   |  .  3  .  . |   |  .  .  2  . |   |  .  .  . 13 |
   |  5  .  .  . |   |  . 10  .  . |   |  .  . 11  . |   |  .  .  .  8 |
   |  9  .  .  . |   |  .  6  .  . |   |  .  .  7  . |   |  .  .  . 12 |
   |  4  .  .  . |   |  . 15  .  . |   |  .  . 14  . |   |  .  .  .  1 |
   +-------------+   +-------------+   +-------------+   +-------------+

2 diagonals:
   +-------------+   +-------------+
   | 16  .  .  . |   |  .  .  . 13 |
   |  . 10  .  . |   |  .  . 11  . |
   |  .  .  7  . |   |  .  6  .  . |
   |  .  .  .  1 |   |  4  .  .  . |
   +-------------+   +-------------+

4 corner squares:
   +-------------+   +-------------+   +-------------+   +-------------+
   | 16  3  .  . |   |  .  .  2 13 |   |  .  .  .  . |   |  .  .  .  . |
   |  5 10  .  . |   |  .  . 11  8 |   |  .  .  .  . |   |  .  .  .  . |
   |  .  .  .  . |   |  .  .  .  . |   |  9  6  .  . |   |  .  .  7 12 |
   |  .  .  .  . |   |  .  .  .  . |   |  4 15  .  . |   |  .  . 14  1 |
   +-------------+   +-------------+   +-------------+   +-------------+

(1+1+1): central square & a (hollow) square & "1514" + opposing fields:
   +-------------+   +-------------+   +-------------+
   |  .  .  .  . |   | 16  .  . 13 |   |  .  3  2  . |
   |  . 10 11  . |   |  .  .  .  . |   |  .  .  .  . |
   |  .  6  7  . |   |  .  .  .  . |   |  .  .  .  . |
   |  .  .  .  . |   |  4  .  .  1 |   |  . 15 14  . |
   +-------------+   +-------------+   +-------------+

2 twisted squares:
   +-------------+   +-------------+
   |  .  3  .  . |   |  .  .  2  . |
   |  .  .  .  8 |   |  5  .  .  . |
   |  9  .  .  . |   |  .  .  . 12 |
   |  .  . 14  . |   |  . 15  .  . |
   +-------------+   +-------------+

4 kites:
   +-------------+   +-------------+   +-------------+   +-------------+
   |  .  3  .  . |   |  .  .  2  . |   |  .  3  .  . |   |  .  .  2  . |
   |  5  . 11  . |   |  . 10  .  8 |   |  .  .  .  . |   |  .  .  .  . |
   |  .  .  .  . |   |  .  .  .  . |   |  9  .  7  . |   |  .  6  . 12 |
   |  . 15  .  . |   |  .  . 14  . |   |  . 15  .  . |   |  .  . 14  . |
   +-------------+   +-------------+   +-------------+   +-------------+

------------------------------------------------------------------------
reinhard.zumkeller@gmail.com, Jun 20 2013