Mensa IQ Test Mensa IQ Visual Pattern Analysis 3 — Questions and Answers
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?
- 3 colors (Correct answer)
- 2 colors
- 4 colors
- 6 colors
Correct answer: 3 colors
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?
- 14 (Correct answer)
- 10
- 12
- 16
Correct answer: 14
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?
- Same as the original 'L' (Correct answer)
- Upside-down 'L'
- Mirror image of original
- Rotated 90° from original
Correct answer: Same as the original 'L'
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?
- 8 white tiles (Correct answer)
- 7 white tiles
- 13 white tiles
- 5 white tiles
Correct answer: 8 white tiles
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?
- 48π (Correct answer)
- 16π
- 32π
- 64π
Correct answer: 48π
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.
Question 6: In a visual grid, every third cell is shaded. If the grid is 6×6 and shading starts at cell (1,1), how many cells are shaded?
- 12 (Correct answer)
- 6
- 18
- 9
Correct answer: 12
In a 6×6 grid with 36 cells total, if every 3rd cell is shaded (counting left to right, top to bottom), then 36/3 = 12 cells are shaded.
Mensa IQ Test Mensa IQ Visual Pattern Analysis 3
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?