Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 2 — Questions and Answers
Question 1: A square paper is folded in half along the vertical center line (right half folds onto left). A rectangular notch is cut from the right edge (the folded edge) of the folded paper. When unfolded, the cutout is shaped like a:
- Narrow rectangle centered on the paper (Correct answer)
- Square in the top-right corner
- Two separate rectangles on the left and right edges
- L-shape
Correct answer: Narrow rectangle centered on the paper
When the right edge (fold) is cut and the paper is unfolded, the cut opens symmetrically to create one rectangle spanning the center of the full sheet.
Question 2: On a standard die, if the 1 is on top and 2 faces you, which number is on your left?
- 3 (Correct answer)
- 4
- 5
- 6
Correct answer: 3
With 1 on top and 2 facing you on a right-handed standard die, the face on your left is 3.
Question 3: A 4×4×4 cube is painted red on all outer faces, then cut into 64 unit cubes. How many unit cubes have exactly two red faces?
- 24 (Correct answer)
- 16
- 8
- 32
Correct answer: 24
Unit cubes with exactly two painted faces are the edge pieces (not corners): each edge of the cube has 2 inner pieces × 12 edges = 24 edge-only pieces.
Question 4: A square piece of paper is folded along its diagonal so the bottom-right corner meets the top-left corner. A hole is punched at the exact center of the folded triangle. When unfolded, where is/are the hole(s)?
- Two holes symmetric about the diagonal fold (Correct answer)
- One hole at the center of the paper
- Four holes at the corners
- One hole in the upper-left quadrant
Correct answer: Two holes symmetric about the diagonal fold
A diagonal fold creates two layers; a single punch makes two holes that are mirror images across the diagonal when unfolded.
Question 5: Two dice are placed side by side. The left die shows 4 on top; the right die shows 2 on top. The faces touching between the two dice (left die's right face and right die's left face) must together sum to:
- 7
- 14
- 6
- Cannot be determined (Correct answer)
Correct answer: Cannot be determined
The touching faces belong to different dice; there is no rule forcing them to sum to any fixed number — only opposite faces on the SAME die sum to 7.
Question 6: A cube net looks like a 'T': one row of 4 squares across the top and one square hanging below the second square from the left. Which square is opposite the leftmost square in the top row?
- The 4th (rightmost) square in the top row (Correct answer)
- The hanging square below
- The 2nd square in the top row
- The 3rd square in the top row
Correct answer: The 4th (rightmost) square in the top row
In a T-net with 4 in a row, the two end squares of the top row (1st and 4th) become opposite faces when the net is folded.
Question 7: A 3×3×3 cube is assembled from 27 unit cubes. How many unit cubes have NO painted faces (assuming only the outer surface is painted)?
- 1 (Correct answer)
- 8
- 0
- 6
Correct answer: 1
Only the single center cube hidden inside the 3×3×3 cube has no faces on the outer surface and therefore no painted faces.
Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 2
A square paper is folded in half along the vertical center line (right half folds onto left).
A rectangular notch is cut from the right edge (the folded edge) of the folded paper.
When unfolded, the cutout is shaped like a: