Mensa IQ Cube, Dice and Paper Folding Flashcards

A square piece of paper is folded in half (bringing the top edge to the bottom edge), then in half again (left edge to right edge). A small triangle is cut from the single closed corner (all folds meet here). When unfolded, the cutout forms a:

Answer: Diamond (rhombus) shape at the center

The closed corner after two rectangular folds is the center of the original sheet; cutting a triangle there creates a small diamond/rhombus cutout at the center when unfolded.

A 3×3×3 cube painted on all outer faces is cut into 27 unit cubes. How many unit cubes have exactly 0 painted faces?

Answer: 1

Only the single center cube of a 3×3×3 is completely interior with no face touching the outside — it has zero painted faces.

On a standard die, if 2 is on top and 3 faces you (toward the south), which number faces east (to your right)?

Answer: 6

With 2 on top and 3 facing south on a standard right-handed die, the east face is 6, following standard die orientation rules.

A rectangular paper is folded so that the shorter edges meet. Then it is folded again the same way. Three holes are punched through all layers in a row. When fully unfolded, how many holes are there?

Answer: 12

Two folds create 4 layers; each of 3 punches through 4 layers creates 4 holes, yielding 3 × 4 = 12 holes total.

A cube is viewed from the top-right-front corner, revealing 3 faces. The top face shows a circle, the front face shows a triangle, the right face shows a square. When the cube is flipped upside down (rotated 180° around the front-back axis), what shape appears on the new top face?

Answer: The symbol on the original bottom face (opposite circle)

Flipping upside down brings the original bottom face to the top; since circle was on top, its opposite face (whatever is on the bottom) is now on top.

A 5×5×5 cube is painted on all outer faces, then cut into 125 unit cubes. How many unit cubes have no painted faces?

Answer: 27

The unpainted interior of a 5×5×5 cube is a 3×3×3 core = 27 unit cubes with no paint.

A die with 1 on top and 2 facing east is tipped north (away from you) twice in a row (two 90° tilts northward). What number is now on top?

Answer: 6

Tipping north once brings the north face to the top and the top to the south face. Tipping north again brings the new north face (originally the bottom) to the top. Since 1 was on top and 6 is opposite, after two north tips: top→south, bottom(6)→north, front→top... after 2 tips northward: the original bottom (6) is now on top.