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Spatial items: rotation, folding and cubes

Spatial items ask you to transform an object in your head and report the result. Most are solvable with a rule instead of imagination.

Painted cube problems

For an n-cube cut into unit cubes, corners have three painted faces (always 8), edges have two (12 times n minus 2), faces have one, and the interior has none, an (n−2) cube.

Folding and punching

Each fold doubles the number of holes. Two folds and one punch gives four holes, arranged symmetrically about the fold lines.

Rotation under time

Track a single feature through the rotation rather than the whole shape. One corner or one arrow is enough to eliminate most options.

Sit the paper — 20 items, 15 minutes

Scored against age, education and area norms. Free certificate with a QR code anyone can verify.

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Questions people ask

Can spatial skill be improved?

Test performance improves quickly with practice on the specific format.

Do these need drawing?

Scratch paper helps on folding items and is not prohibited.

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