Project the whole solid

Combine every depth layer before choosing an opening.

Look along the arrow

Every stack is filled from bottom to top. Look along the travel arrow from the solid’s side. This simple solid has one depth layer; its outline has column heights 3, 2 and 1.

You may turn it in 90° steps around the arrow before moving. The second outline shows one clockwise turn. Then keep that orientation and slide straight, without tilting, twisting, reflecting or resizing.

Look in the arrow’s direction.
Along the arrow
One clockwise quarter-turn

Combine the depth layers

This solid has three depth layers. Viewed along the arrow, their column heights are 3, 1, 0; then 2, 2, 1; then 0, 1, 0. A zero means an empty column.

Keep every position occupied in any layer. The combined heights are 3, 2, 1, so the opening needs six squares. Overlapping positions count once. No single layer shows the full outline.

Include cubes at every depth.
Layer 1
Layer 2
Layer 3
Whole outline

Try a different solid

Use the arrow to find this new solid’s whole outline. Each stack is still filled all the way down.

Both openings have seven squares. You may choose a quarter-turn before moving, but must then pass straight through. Which opening fits?

Turn first, then slide straight.
Opening A
Opening B

Try it

Which opening can the whole solid pass through?

  1. Opening A.
  2. Opening B.
Show the answer

Opening B.

B matches the full outline after one clockwise quarter-turn. Before turning, the combined heights are 4, 2, 1. A has the same area, but a different shape.

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