Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 4

Question 1

A cube net is shaped like a plus sign (+): one center square with one square on each of its four sides, and one additional square attached to the bottom extension. Which of the following is true?

Accepted Answer

The top extension and bottom extension squares are opposite faces

Answer

In a plus-sign net with an extra square on one arm, the two extensions directly opposite each other across the center fold into opposite faces — the top and bottom arm squares become opposite faces.

Question 2

A die shows 1 on top, 2 on front, and 3 on the right. Is this a valid standard (right-handed) die orientation?

Accepted Answer

No — standard dice have 1, 2, 3 meeting at a vertex going counterclockwise

Answer

On a standard right-handed die, the faces 1, 2, 3 meet at a vertex in counterclockwise order when viewed from that vertex; if they appear clockwise it's a left-handed (mirror) die.

Question 3

Three unit cubes are glued in an L-shape: two in a row and one on top of the first. How many unit square faces are exposed on the outside of this solid?

Accepted Answer

14

Answer

Each unit cube has 6 faces; 3 cubes share 2 glue joints (each hiding 2 faces total), so exposed = 3×6 - 2×2 = 18 - 4 = 14 faces.

Question 4

A square paper is folded along the vertical center, then the top-right corner of the folded paper is folded down to touch the bottom edge. A hole is punched through all layers at the new folded corner tip. How many holes appear when fully unfolded?

Accepted Answer

4

Answer

The first fold creates 2 layers; the second fold of the corner creates 2 more layers in that region (4 total); one punch through 4 layers yields 4 holes.

Question 5

A 3×3×3 cube is dipped in paint (all outer faces painted), then the top layer of 9 unit cubes is removed. How many of those 9 removed unit cubes have exactly 2 painted faces?

Accepted Answer

4

Answer

The top layer has 1 center (1 painted face), 4 edge pieces (2 painted faces each), and 4 corner pieces (3 painted faces each); so 4 unit cubes have exactly 2 painted faces.

Mensa Practice Test Practice Test

Mensa Practice Test Practice Test

Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 4