Question

Which of the designs best completes the following sequence?

• A.
• B.
• C.
• D.

Hint:

Track how the outer and middle boundary shapes and the fill patterns rotate between circle and hexagon across the three figures.

Answer 1

The Correct Option is A

Treat each figure as four independent two-state switches: outer boundary shape (circle or hexagon), outer fill (dots or stripes), middle boundary shape (circle or hexagon), and inner fill (dots or stripes).

1. List the state of each switch in figure 1, figure 2 and figure 3. Across these three figures every switch flips at least once, though not all switches flip together.
2. Since each switch only has two possible states, a switch that has moved from its figure-1 state to a new state in figure-2, and back again in figure-3 (or the reverse pattern), tells you exactly what state it must take next: it simply flips again from its figure-3 state.
3. Apply this flip to all four switches independently: outer boundary flips from its figure-3 state, outer fill flips, middle boundary flips, and inner fill flips.
4. Compare the resulting combination of four states against each option. Only one option reproduces this exact combination on all four switches at once.

Checking option by option, option (1) is the only figure where the outer boundary, outer fill, middle boundary and inner fill are all consistent with continuing the rotation seen from figure 1 through figure 3. The other three options each get one of the four switches wrong. So the missing figure is $\boxed{\text{option (1)}}$.