Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 6

Question 1

In a standard die, the number 1 is opposite 6, 2 is opposite 5, and 3 is opposite 4. A die shows 5 on top. The sum of the five visible faces (top + four sides) is:

Accepted Answer

15

Answer

Total of all faces = 21; the hidden bottom face opposite 5 is 6; so the 5 visible faces sum to 21 - 6 = 15.

Question 2

A square paper is folded so the bottom-left corner touches the top-right corner (diagonal fold). A hole is punched in the top-left corner of the folded triangle. When unfolded, how many holes are there and where?

Accepted Answer

2 holes — one at top-left and one at bottom-right of the paper

Answer

Folding bottom-left to top-right folds along the other diagonal; the top-left corner of the folded shape corresponds to the original top-left and its mirror — punching there creates 2 holes at top-left and bottom-right.

Question 3

How many unit cubes in a 4×4×4 cube have exactly 1 painted face (assuming all outer surfaces are painted)?

Accepted Answer

24

Answer

1-face cubes are the center squares of each face: each face of a 4×4×4 cube has a 2×2 region of face-only pieces = 4 per face × 6 faces = 24.

Question 4

A die is standing with 3 facing up and 6 facing the observer. It rolls once to the right (eastward tilt 90°). What now faces the observer?

Accepted Answer

6

Answer

Rolling east tilts the die around the north-south axis; the front face (6, facing the observer) does not change — 6 still faces the observer.

Question 5

A net consists of 2 rows of 3 squares (2×3 grid). Which statement is true?

Accepted Answer

This net cannot fold into a cube because two faces would overlap

Answer

A 2×3 grid of 6 equal squares cannot fold into a cube — two faces inevitably overlap, making it an invalid cube net.

Mensa Practice Test Practice Test

Mensa Practice Test Practice Test

Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 6