Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 3 — Questions and Answers
Question 1: A die is rolled from its starting position (6 on top, 1 facing north) one step south, then one step east. What number is on top after both rolls?
- 2 (Correct answer)
- 3
- 5
- 4
Correct answer: 2
Rolling south brings the south face (initially 2, since 2 is opposite 5 and 1 faces north on standard die) to the top after the first roll; then rolling east from that position brings 2 to the top.
Question 2: A strip of 6 squares in a row is a valid cube net. If the leftmost square is labeled A and the rightmost is labeled F, which pair of squares becomes opposite faces?
- A and D (Correct answer)
- A and F
- B and E
- C and F
Correct answer: A and D
In a linear strip of 6 squares, squares 1 apart after wrapping become opposite: A(1) is opposite D(4), B(2) is opposite E(5), C(3) is opposite F(6).
Question 3: A rectangular piece of paper is folded in thirds (left third folds over middle, then right third folds over). A circular punch is made through all layers in the center. How many holes appear when fully unfolded?
- 3 (Correct answer)
- 6
- 4
- 2
Correct answer: 3
Folding in thirds creates 3 layers; one punch creates 3 holes when fully unfolded.
Question 4: A 2×2×2 cube is painted on all outer faces, then cut into 8 unit cubes. How many unit cubes have exactly 3 painted faces?
- 8 (Correct answer)
- 4
- 0
- 6
Correct answer: 8
In a 2×2×2 cube, every unit cube is a corner piece, so all 8 unit cubes have exactly 3 painted faces.
Question 5: If a die has 3 on top and 5 facing you, and is then rotated 90° clockwise (viewed from above) without tilting, what number now faces you?
- 6 (Correct answer)
- 1
- 4
- 2
Correct answer: 6
A 90° clockwise rotation (viewed from top) moves the face that was to the left to face you; with 3 on top and 5 toward you on a standard die, 6 is to the left, so 6 now faces you.
Question 6: A square paper is folded so the top edge meets the bottom edge, then folded again so the left edge meets the right edge. A rectangular notch is cut from the bottom-left corner (the completely closed corner). When unfolded, the cutout forms a:
- Square in the center of the paper (Correct answer)
- Rectangle in the center
- Four corner squares
- Single rectangle at bottom-left
Correct answer: Square in the center of the paper
The fully closed corner after two folds corresponds to the exact center of the original paper; cutting there creates one square hole in the center when unfolded.
Question 7: How many edges does a cube have?
- 12 (Correct answer)
- 8
- 6
- 16
Correct answer: 12
A cube has 6 faces, 8 vertices, and 12 edges — this is a fundamental property of a cube.
Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 3
A die is rolled from its starting position (6 on top, 1 facing north) one step south, then one step east.
What number is on top after both rolls?