BLOCK PARTY
BUILDING OUT
Each series below shows the first three shapes in a progressive sequence. For instance, in series A the shapes increase from 1 to 6 and then to 18 cubes. How many cubes are in the next shape in each sequence? You may assume that hidden cubes are where you expect them to be.
A [Easy}
1
6
18
B [Challenging}
1
6
19
C [Difficult]
 54 |  48 |  42 |
FOLDING IN
Find pairs of patterns below that could be folded to create identical cubes. For instance, the two patterns above could both be folded into a cube with targets on adjacent faces.
A [Easy] Hint: Count the squares of each color.
B [Challenging] Hint: Some letters look the same no matter how they’re rotated.
C [Difficult] Hint: The red dots are always on opposite faces.
STACKING UP Fit each figure below with another figure to complete a solid 3 x 3 x 2 block. You can rotate figures—for example, figure f can be rotated to fit into figure a—but you can’t use mirror reflections to complete a figure. In some cases a figure can fit with a copy of itself to form a block. Hint: Think of each figure in terms of a top layer of cubes and a bottom layer of cubes. 
 a |  b |  c |  d |
 e |  f |  g |  h |
 i |  j |  k |  l |
