Mensa IQ Spatial Reasoning and Patterns Flashcards

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

Answer: Square

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.

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?

Answer: 12

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.

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

Answer: Brick or offset tiling

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

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?

Answer: Cube

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).

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

Answer: 162

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

A shape is rotated 90° clockwise, then reflected over a vertical axis. Which single transformation is equivalent to this combined operation?

Answer: Reflection over a horizontal axis

A 90° clockwise rotation followed by a vertical reflection is equivalent to a single reflection over a horizontal axis.

Which figure completes the analogy: solid square is to hollow square as solid circle is to ___?

Answer: Hollow circle

The analogy transforms a filled shape into its outline equivalent, so a solid circle becomes a hollow (outline) circle.