Mensa IQ Test Mensa IQ Visual Pattern Analysis 3

Question 1

In a tiling pattern, every cell is colored using 3 colors such that no two adjacent cells share the same color. What is the minimum number of colors needed to color a hexagonal grid?

Accepted Answer

3 colors

Answer

A regular hexagonal grid (where each hexagon touches 6 others) can be 3-colored such that no adjacent hexagons share a color. This is because hexagonal grids are 3-colorable by their structure. Two colors are insufficient since odd cycles exist.

Question 2

A spiral pattern starts at the center and winds outward. Each complete revolution adds 4 more dots than the previous revolution. Revolution 1 has 6 dots. How many dots does Revolution 3 have?

Accepted Answer

14

Answer

Revolution 1: 6 dots. Revolution 2: 6+4 = 10 dots. Revolution 3: 10+4 = 14 dots. The count increases by a constant 4 per revolution.

Question 3

A pattern alternates between two transformations: reflect horizontally, then rotate 90° clockwise. Starting with an 'L' shape, what does it look like after 4 transformations?

Accepted Answer

Same as the original 'L'

Answer

Step 1: reflect horizontally (reversed L). Step 2: rotate 90° CW. Step 3: reflect horizontally. Step 4: rotate 90° CW. The combination of H-reflect + 90°CW repeated twice brings us back to the original orientation.

Question 4

A visual sequence shows: 1 black tile, 1 white tile, 2 black tiles, 3 white tiles, 5 black tiles. How many tiles are in the next group?

Accepted Answer

8 white tiles

Answer

The counts follow the Fibonacci sequence: 1, 1, 2, 3, 5, 8. The colors alternate between groups. The 6th group has 8 tiles, and since it alternates: black, white, black, white, black, white — the 6th group is white.

Question 5

A pattern shows concentric circles where each new circle has double the radius of the previous. If the innermost circle has radius 1, what is the area of the ring between the 3rd and 4th circles?

Accepted Answer

48π

Answer

Radii: r₁=1, r₂=2, r₃=4, r₄=8. Area of 4th circle: π(8²)=64π. Area of 3rd circle: π(4²)=16π. Ring area = 64π - 16π = 48π.

Mensa Practice Test Practice Test

Mensa Practice Test Practice Test

Mensa IQ Test Mensa IQ Visual Pattern Analysis 3