Solution - Cubism

by Derek Kisman and Craig Kasper

Answer: Click here to reveal

As should be quickly evident, this is a 3D version of a Fences (or Slitherlink) puzzle. Instead of creating a linear border (the "fence") surrounding a 2D planar region, you must create a surface that encloses a 3D volume. Each layer represents one "slice" of a 7x7x7 cube; each number in a cell indicates the number of surface "walls" directly adjacent to the cell (in all 6 directions).

There aren't really any tricks, but you will need to use the fact that the surface can't touch itself. The most obvious way this can happen is along an edge (so a 2x2x1 pattern of OX/XO is impossible). More subtly, it also can't touch itself at a vertex (so a 2x2x2 pattern of OX/OO OO/XO is also impossible). The surface is also connected and has no internal holes, but this information is not necessary to solve the puzzle.

After solving the puzzle, you'll notice that the enclosed volume is a cube with 7 connected regions removed. The regions are ordered on the last layer in an obvious way (top-bottom). The sizes of the regions are 20, 9, 7, 18, 9, 19, and 8. So the final answer is TIGRISH.