Spatial reasoning and assembly · SET 9

Which cube can be made by folding the net? Match both neighbouring faces and the directions of their symbols.

AI reconstruction. Which piece exactly fills the white gap to complete the hexagonal-cell pattern, with no gaps or overlap? All small hexagons are congruent. You may translate and rotate a piece in the plane in multiples of 60 degrees, but you may not turn it over or reflect it. Keep the existing colored central cell.

The grey box shows three views of the same cube. Which option replaces the blank face in the third view? Keep each symbol’s orientation.

Which option shows the flat two-dimensional view from the back, following the arrow? Blocks directly behind one another overlap in this view.

Which option is the flat view of the solid from directly above? Keep all visible block boundaries and show spots only if they are on upward-facing surfaces.

AI reconstruction. Look straight down at the pink cube construction. Count each occupied vertical column once and keep genuinely empty columns empty. Assume no extra hidden columns; compare the footprints in the orientation shown.

AI reconstruction. Follow the folds in order: fold the left half to the right; fold the top and bottom thirds into the middle third; then fold the remaining packet in half from left to right. Cut the shown small rectangular notch through every layer at the new left fold. Unfold completely. Which pattern results? The answer pictures show the opened sheet turned through a quarter-turn; this change of display orientation is allowed. Compare the hole arrangement and hole orientations only; treat the outer sheet dimensions in the answer drawings as schematic, not to scale.

The first picture is the target. Which option can be added to the piece in the grey box to make exactly that target, without rotating either piece? Slide the chosen piece into place without overlap.

Which set of pieces can be assembled into the solid on the left? You may rotate whole pieces, but cannot cut them or change the visible joins.

The first picture is the target. Which option can be added to the piece in the grey box to make exactly that target, without rotating either piece? Slide the chosen piece into place without overlap.

AI reconstruction (instruction): Follow the folding and cutting sequence, then unfold the circle completely. Added geometric interpretation: fold left to right, then top to bottom, then bisect the lower-right quarter into an eighth. The cut near the center is a rounded tip cut; the other is a rectangular notch on the sloping folded edge. Cut through all layers. Which result matches?

AI reconstruction. Choose the missing connected piece. Reconstructed goal: complete a rectangle six cubes wide, four cubes high and one cube thick. Every pictured cube stays in its shown position. The left three columns must be green and the right three blue. Insert one option by translation only, in the displayed orientation; do not rotate, reflect, overlap or move existing cubes.

Which set of pieces can be put together to make the solid on the left? You may turn the pieces, but cannot cut them or overlap them.

Which cube can be made by folding the net? Match both neighbouring faces and the directions of their symbols.

AI reconstruction: Superimpose the two triangular grids without rotating or reflecting them. A small triangle is green in the result if it is green in either input; otherwise it stays white. Which option is the result?

Which shape A, B, C or D is the flat net of the hexagonal box shown?

Which option is the same three-dimensional solid as the target after rotation? Keep all colours, piece lengths and connections unchanged.

Which option shows the solid in the grey box viewed from the right, in the direction of the dotted arrow? Preserve every piece and seam.

A rectangular box measures 1 m × 1 m × 50 cm. How many such boxes can fit in a rectangular container with internal dimensions 9 m × 5 m × 3 m? Treat the given box sizes as exact outer dimensions and allow face-to-face packing without gaps.

The grey box shows three views of the same cube. Which option replaces the blank face in the third view? Match the positions and directions of the markings.