Mensa IQ Spatial Reasoning and Patterns Flashcards

A matrix has 3 rows and 3 columns. Row 1: △ ○ □ | Row 2: ○ □ △ | Row 3: □ △ ? What shape belongs in the bottom-right cell?

Answer: Circle

Each row and column contains each of the three shapes exactly once (Latin square pattern), so the missing shape must be ○ (circle).

How many squares of ALL sizes are in a 4×4 grid of unit squares?

Answer: 30

A 4×4 grid contains 16 (1×1) + 9 (2×2) + 4 (3×3) + 1 (4×4) = 30 squares total.

A spiral pattern grows outward: the 1st ring has 8 cells, the 2nd ring has 16 cells, the 3rd ring has 24 cells. How many cells does the 5th ring have?

Answer: 40

Each ring adds 8 more cells than the previous (arithmetic sequence with common difference 8), so the 5th ring has 8 × 5 = 40 cells.

An object viewed from the front appears as a circle, from the side as a rectangle, and from the top as a rectangle. What 3D shape is it?

Answer: Cylinder

A cylinder has a circular front view and rectangular side and top views.

In a pattern of alternating black and white triangles arranged in a row, the 1st is black, 2nd white, 3rd black… What color is the 44th triangle?

Answer: White

Even-numbered positions are white in this alternating pattern, and 44 is even, so the 44th triangle is white.

A shape undergoes 4 successive 90° clockwise rotations. What is the net result?

Answer: Back to the original orientation

Four 90° clockwise rotations total 360°, returning the shape to its original orientation.

In a 5×5 grid, how many unique paths exist from the top-left corner to the bottom-right corner if you can only move right or down?

Answer: 70

Moving from corner to corner in a 5×5 grid requires 4 rights and 4 downs; the number of paths is C(8,4) = 70.