## Pile of Tiles

by Jessen Yu

Each tile is a unique slice through a 7x7x7 cube which has a black and white lattice pattern throughout. The first twelve tiles are slices through the majority-white layers and the clues provide answers for the white spaces. The remaining nine tiles are through the interleaved majority-black layers, with clues provided for the black spaces. Solvers need to reassemble the cube (the two sets can be solved separately) by figuring out how the slices fit together. As an aid, within each set, the tiles are presented alphabetically by the first clued across answer.

If we call the axes X, Y, and Z along the edges of the cube, the grids are always presented in one of three orientations of slicing:

• Across = X, Down = Y
• Across = Y, Down = Z
• Across = Z, Down = X

When finally assembled, solvers should notice that the two grid types are complementary and can be combined into one cube. There are three ways to combine the two pieces while keeping the Across and Down directions consistent, but the diagonal is invariant to all of the rotations. Reading down the diagonal of the cube gives the answer: ANT HEAP

Here are the three rotations of the first set of tiles. The left column is Across=X, Down=Y, the second column is Across=Y, Down=Z, and the last is Across=Z, Down=X. All three columns are presented stacked along the remaining axis.

Here are the three rotations for the second set of tiles.

And the merged complete cube (XY slices), with highlighted diagonal.