Daily Math Puzzle: 2026-05-21

9 — We need the number of ways to pair the four helmets with the four gloves so that no helmet is matched with a glove of the same color, and the order of the four days matters. This is a classic derangement problem for 4 items. The number of derangements D₄ is: D₄ = 4! \left(1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!}\right) = 24 \left(1 - 1 + 0.5 - 0.1667 + 0.0417\right) = 24 \times 0.375 = 9. Thus there are 9 distinct ways to assign the helmets to gloves without any matching colors, and each assignment corresponds to a unique ordered sequence for the four days. Therefore the correct answer is 9, which is choice C (index 2).