Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 5

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?

Accepted Answer

8

Answer

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?

Accepted Answer

8

Answer

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?

Accepted Answer

Cannot be determined

Answer

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?

Accepted Answer

4

Answer

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.

Accepted Answer

C only

Answer

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.

Mensa Practice Test Practice Test

Mensa Practice Test Practice Test

Mensa IQ Test Mensa IQ Cube, Dice and Paper Folding 5