Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 4 — Questions and Answers
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?
- The center square and the extra bottom square are opposite faces
- The top extension and bottom extension squares are opposite faces (Correct answer)
- The left and right extension squares are opposite faces
- All four extensions are on the same face
Correct answer: The top extension and bottom extension squares are opposite faces
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?
- No — standard dice have 1, 2, 3 meeting at a vertex going counterclockwise (Correct answer)
- Yes — any three faces can appear this way
- No — 1, 2, 3 cannot share a vertex
- Yes — but only if 4, 5, 6 are on the opposite faces
Correct answer: No — standard dice have 1, 2, 3 meeting at a vertex going counterclockwise
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?
- 14 (Correct answer)
- 12
- 8
- 14
Correct answer: 14
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?
- 4 (Correct answer)
- 2
- 3
- 1
Correct answer: 4
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?
- 4 (Correct answer)
- 8
- 1
- 0
Correct answer: 4
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.
Question 6: If a die is placed with 4 on top and rolled north, then east, then south, what number is on top after all three moves?
- 4 (Correct answer)
- 6
- 1
- 3
Correct answer: 4
Rolling north, then east, then south traces three sides of a 'square route'; the net rotation brings the die back so the original top (4) returns to the top after these three perpendicular moves.
Question 7: A cube net consists of a row of 4 squares (positions 1–4 left to right) with one square below position 2 and one square above position 3. When folded, which square is opposite position 1?
- Position 4 (Correct answer)
- Position below 2
- Position above 3
- Position 3
Correct answer: Position 4
In this net, positions 1 and 4 are the two ends of the 4-square row and fold into opposite faces of the cube.
Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 4
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?