Mensa Mensa IQ Spatial Reasoning and Patterns 4

Question 1

A sequence of shapes follows this rule: circle, square, triangle, circle, square, triangle… What is the 17th shape in the sequence?

Accepted Answer

Square

Answer

The sequence repeats every 3 shapes; 17 mod 3 = 2 (since 3×5=15, remainder 2), which maps to position 2 in the cycle — square.

Question 2

A 3D cube is painted red on all faces, then cut into 27 equal smaller cubes. How many small cubes have exactly 2 red faces?

Accepted Answer

12

Answer

Edge pieces (not corner) of a 3×3×3 cube have exactly 2 painted faces; there are 12 edges on a cube, each contributing 1 such piece.

Question 3

Looking at a grid pattern where odd rows shift right by half a unit, what type of tiling is described?

Accepted Answer

Brick or offset tiling

Answer

Offsetting alternating rows by half a unit creates a brick-bond (running bond) tiling pattern.

Question 4

A flat cross-shaped net is folded into a 3D shape. The cross has one center square and four squares extending from each side. What shape does it form?

Accepted Answer

Cube

Answer

A cross-shaped net with one center square and four arms folds into a cube (one face remains open unless a sixth square is added, but the standard 6-square cross net forms a cube).

Question 5

In a number pattern: 2, 6, 18, 54, ___ . What comes next?

Accepted Answer

162

Answer

Each term is multiplied by 3 (geometric sequence with ratio 3), so 54 × 3 = 162.

Mensa Practice Test

Mensa Practice Test

Mensa Mensa IQ Spatial Reasoning and Patterns 4