Problem Solving: Figure Series Flashcards

In a series, figures alternate between two forms: X inside a circle (odd figures) and a circle inside an X (even figures). Figure 1 shows X inside a circle. What does figure 6 show?

Answer: Circle inside an X

Even-numbered figures show a circle inside an X, so figure 6 follows this even-position pattern.

In a figure series, the number of shaded squares follows the Fibonacci sequence: 1, 1, 2, 3, 5, ... How many squares are shaded in figure 6?

Answer: 8

Each Fibonacci term is the sum of the two before it: 1, 1, 2, 3, 5, 8 — figure 6 has 8 shaded squares.

A series shows a shape and its mirror image side by side. Each step, both shapes rotate 180°. If figure 1 shows (▶ ◀), what does figure 3 show?

Answer: ▶ ◀

Two rotations of 180° total 360°, returning the pair to its original orientation (▶ ◀).

A figure series shows the perimeter of a square doubling each step. If figure 1 has a perimeter of 4 cm, what is the perimeter in figure 4?

Answer: 32 cm

Doubling each step: 4, 8, 16, 32 — figure 4 has a perimeter of 32 cm.

A figure shows a repeating row of symbols: ★☆★☆★☆★☆ ... Following this pattern, what is the 10th symbol?

Answer: ☆ (empty star)

Odd positions hold filled stars (★) and even positions hold empty stars (☆); position 10 is even.

In a figure series, a triangle is flipped vertically (top-bottom) with each step. Figure 1 shows △ (pointing up). What does figure 4 show?

Answer: ▽ (pointing down)

Flipping each step: △→▽→△→▽; figure 4 is in the flipped (downward) position.

A hexagonal dot pattern grows by adding a new outer ring each step. Figure 1: 1 dot; figure 2: 7 dots (+6); figure 3: 19 dots (+12). The next ring adds 18 dots. How many dots are in figure 4?

Answer: 37

Figure 4 = figure 3 + 18 = 19 + 18 = 37 dots.