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When the following shape is folded to form a cube, which is the only one of the options from A to D that can be produced ?

A cube net of six squares: a black dot face above a face with both diagonals; to the right of that face, a face with one diagonal, a black dot on a horizontal line, and a white circle on a vertical line; below it, a white circle on a horizontal line.

Options from A to D

  • A.A drawn cube: a black dot on the top face, crossing diagonals on the left face and a white circle on a vertical line on the right face
  • B.A drawn cube: a black dot on the top face, diagonals on the left face and crossing diagonals on the right face
  • C.A drawn cube: a black dot on a line on the top face, and a white circle on a horizontal line on each of the left and right faces
  • D.A drawn cube: a plain top face with a line, a black dot on a vertical line on the left face and a white circle on a vertical line on the right face

Answer: C

The only cube that can be produced is C.

Fold the net with the X face (both diagonals) in front and the plain black-dot face on top. Then the single-diagonal face is on the right, the dot-on-a-line face at the back, the circle with a vertical line on the left, and the circle with a horizontal line underneath.

  • A shows the black-dot top with the X face and, to its right, the circle with a vertical line; but that circle face lies to the left of the X face.
  • B shows the black-dot top with the single-diagonal face to the left of the X face; it belongs on the right.
  • D has the single-diagonal face on top and the dot-on-a-line face on the left. Turned that way, the face to the right of the dot-on-a-line face is the plain black-dot face, not a circle.
  • C shows the dot-on-a-line face on top above the two circle faces. These three faces meet at one corner of the folded cube, and turning the cube so that the dot-on-a-line face is on top puts the horizontal-line circle on the left and the vertical-line circle on the right, each with its line running horizontally, exactly as drawn.

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