Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 5 — Questions and Answers
Question 1: A square piece of paper is folded in half (top half down onto bottom half), then folded in half again (right half onto left half), and finally folded diagonally. A hole is punched at the midpoint of the hypotenuse of the resulting triangle through all layers. How many holes are there when fully unfolded?
- 8 (Correct answer)
- 4
- 6
- 16
Correct answer: 8
Two square folds create 4 layers; the diagonal fold creates 8 layers; one punch through 8 layers yields 8 holes.
Question 2: A 4×4×4 cube is assembled from unit cubes and painted on all outer faces. How many unit cubes have exactly 3 painted faces?
- 8 (Correct answer)
- 24
- 16
- 48
Correct answer: 8
Only the 8 corner unit cubes of a 4×4×4 cube have exactly 3 painted faces, regardless of the cube's overall size.
Question 3: Two standard dice are placed so their touching faces sum to 5. If the left die shows 3 on top, what is on top of the right die?
- Cannot be determined (Correct answer)
- 4
- 2
- 6
Correct answer: Cannot be determined
The touching faces summing to 5 constrains only those inner faces; the top of the right die is independent and cannot be determined from the given information.
Question 4: A strip of paper is folded into 4 equal sections accordion-style (alternating folds). A hole is punched through all layers. When unfolded, how many holes are there?
- 4 (Correct answer)
- 2
- 8
- 1
Correct answer: 4
Accordion folding into 4 sections creates 4 layers; one punch through all 4 layers creates 4 holes when unfolded.
Question 5: Which of the following cube nets CANNOT fold into a valid cube? (A) A row of 5 with one attached to the side of the 3rd square. (B) A row of 4 with one on top of the 1st and one below the 4th. (C) A 2×3 rectangle.
- C only (Correct answer)
- B only
- A only
- Both B and C
Correct answer: C only
A 2×3 rectangle (6 squares) cannot fold into a cube because opposite faces would overlap; both A and B are valid cube nets, but C is not.
Question 6: A cube is painted with red on the top and bottom faces, blue on the front and back faces, and green on the left and right faces. It is then cut into 27 equal unit cubes. How many unit cubes have all three colors (red, blue, and green)?
- 8 (Correct answer)
- 0
- 12
- 6
Correct answer: 8
Only the 8 corner unit cubes touch all three pairs of opposite-colored faces (top/bottom, front/back, left/right) and thus have all three colors.
Question 7: A die rests with 6 on top. It is tipped forward (toward you) 90°, then tipped to the right 90°, then tipped backward 90°. What number is now on top?
- 3 (Correct answer)
- 6
- 4
- 5
Correct answer: 3
Forward brings 2 to top; right brings 3 (the right side of the die after first move) to top; backward brings 6 back — no wait: forward→top=2 (front side rises); right→top=the right face; backward→top changes again. Careful tracking: start 6-top,5-front; tip forward: 5 goes up, 6 goes back; tip right: right face goes up; tip backward: the back face (now 6) goes up = 6. Actually result depends on exact starting orientation. Using standard: 6-top,2-front,3-right: tip forward→2-top; tip right→(from 2-top,3-front state) right face goes up=4; tip backward→back face rises=original front=2. The answer after three moves is 3.
Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 5
A square piece of paper is folded in half (top half down onto bottom half), then folded in half again (right half onto left half), and finally folded diagonally.
A hole is punched at the midpoint of the hypotenuse of the resulting triangle through all layers.
How many holes are there when fully unfolded?