Mensa IQ Figure Series and Visual Patterns Flashcards

A sequence: [square with no corners cut] → [square with 1 corner cut, making a pentagon] → [square with 2 opposite corners cut, making a hexagon] → [square with 3 corners cut, making a heptagon] → [?]. What comes next?

Answer: Square with all 4 corners cut, making an octagon

One corner is cut per step, adding one side each time (4→5→6→7→8 sides).

A 3×3 matrix: cells contain black dots. The number of dots: Row 1: 1, 2, 3. Row 2: 2, 4, 6. Row 3: 3, 6, [?].

Answer: 9

Each cell value = (row number) × (column number); cell (3,3) = 3×3 = 9.

A sequence of figures: each is a regular polygon with a dot at the center. The dot moves outward to the midpoint of one side each step, while the polygon gains one side. Figure 1: triangle, dot at center. Figure 2: square, dot at midpoint of bottom side. Figure 3: pentagon, dot at midpoint of bottom-right side. Figure 4: [?]

Answer: Hexagon with dot at the midpoint of the next clockwise side

The polygon gains one side each step and the dot moves clockwise to the next side's midpoint.

A sequence of frames, each frame containing a different number of identical small triangles arranged in a triangular grid: Frame 1: 1 triangle. Frame 2: 3 triangles. Frame 3: 6 triangles. Frame 4: 10 triangles. Frame 5: [?]

Answer: 15 triangles

The counts are triangular numbers (1, 3, 6, 10, 15) — each step adds one more triangle than the last.

A figure sequence shows a horizontal bar chart (the bars are part of the figure). Step 1: one bar of height 1. Step 2: two bars, heights 1 and 2. Step 3: three bars, heights 1, 2, and 3. Step 4: [?]

Answer: Four bars with heights 1, 2, 3, and 4

Each step adds one new tallest bar while keeping all previous bars; step 4 has bars of height 1, 2, 3, and 4.

A 3×3 grid: each cell contains a shape (circle, square, or triangle) in one of three sizes (small, medium, large). No row or column repeats a shape OR a size. Row 1: small circle, medium square, large triangle. Row 2: medium triangle, large circle, small square. Row 3: large square, small triangle, [?].

Answer: Medium circle

Row 3 needs a circle (not square or triangle) and the missing size in row 3 is medium; column 3 also confirms medium circle.

A sequence shows figures made of unit squares (like Tetris pieces): Step 1: 1 square. Step 2: 3 squares in an L-shape. Step 3: 6 squares in a staircase. Step 4: 10 squares in a larger staircase. Step 5: [?]

Answer: 15 squares

The figures use triangular numbers of squares (1, 3, 6, 10, 15); each step adds a new row of one more square.