There are \(n\) fish numbered \(1\) through \(n\) at one end of an aquarium. They all start swimming at the same time to the other end of the aquarium. Once a fish reaches an end of the aquarium, it turns around immediately and continues swimming in the other direction.

Fish \(1\) swims with speed \(v_1\), fish \(2\) swims with speed \(v_2 = 2 v_1\), fish \(3\) swims with speed \( v_3 = 2 v_2 \), and so on.

Will the \(n\) fish all be at the same end of the aquarium at the same time again?

An electric field line leaves a positive charge at an angle of \(60^{\circ}\) and enters a negative charge at an angle of \(\theta\). These angles are measured from the straight line joining the two charges.

The magnitude of the positive charge is 4 times the magnitude of the negative charge.

What is \(\theta?\)

Suppose we're playing chess on a \( 2 \times 2 \times 2 \) cube, where the movements of pieces that are considered valid are those that would be valid on a flattened-out net. For example, if a rook is placed on a square, it could reach 13 other squares in one move.

**If a queen is placed on a square, how many squares could it reach in one move?**

**Note:** On a \( 2 \times 2 \times 2 \) cube, each of the squares can equivalently be the starting position. As shown above, as long as a space is accessible on at least one net, it is considered a valid movement.

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