The figure has a centre circle and four rings around it, from the inside out:

• Ring 1: one whole ring
• Ring 2: divided into 6 parts
• Ring 3: one whole ring
• Ring 4: divided into 8 parts

Colouring:

• The 6 parts of ring 2 form an even cycle, so they alternate two colours, 1 and 2.
• Ring 1 and ring 3 each touch all of ring 2, so both get colour 3. (They don't touch each other.)
• The centre touches only ring 1, so it gets colour 1.
• The 8 parts of ring 4 (an even cycle) touch only ring 3 (colour 3), so they alternate colours 1 and 2.

Fewer than 3 colours is impossible, because ring 1 and two adjacent parts of ring 2 all touch each other. So the minimum is 3.

Answer: (A) 3