Goal: Build a tiny 2D engine using value types correctly and observe pitfalls/perf.

Tasks

1. Implement a readonly struct Vector2 with fields double X, Y, constructor, Length, Normalized(), and operators +, -, unary -, scalar *, Dot(in Vector2 a, in Vector2 b), and Deconstruct(out double x, out double y). Ensure no hidden copies and no boxing.
2. Implement a struct BoundingBox with fields Vector2 Min, Max (mutable is fine here). Add Contains(in Vector2 p) and Inflate(double delta).
3. Implement a class Particle with Vector2 Position, Vector2 Velocity, and a read-only double Speed => Velocity.Length. Add void Step(double dt, in BoundingBox bounds) that moves the particle and bounces on edges (invert velocity on collision). Because bouncing only flips a sign, Speed stays constant for the life of a particle, which is what makes the distance total in Task 4 easy to check.
4. Write a Main that creates 100 particles with random velocities inside a 100×100 box and advances them for 1,000 steps, accumulating the total distance traveled.
5. Pitfall demo: Add a public Vector2 this[int i] { get; set; } indexer to a Particles container that stores a List<Vector2> of positions. Demonstrate the forgotten write-back: read an element into a local, produce an updated value, and do not assign it back. The stored element is unchanged and nothing warns you. Then fix it by assigning the local back through the indexer. While you are there, try to write the noisier versions of the same mistake and note the compiler errors you get: mutating a foreach variable and mutating through list[0].X++ are both rejected outright. C# closes those doors; the silent copy-and-forget is the one it leaves open.

Acceptance Criteria

• Vector2 is readonly struct, methods that read only take parameters as in.
• No allocation or boxing in the hot loop (avoid object, ArrayList, LINQ in the inner step).
• The simulation runs and prints the total distance traveled and the final average speed.
• Vector2 overrides ToString() (for example $"({X:F2},{Y:F2})"), so printing a vector shows its values rather than the type name.
• Name the type Vector2 yourself and do not import System.Numerics: the BCL Vector2 is float-based and has no Normalized() instance method, so the two collide.

Checkpoint

• With new Random(1), 100 particles, dt = 0.016 and 1,000 steps, the run prints Total distance: 31873.62 and Final average speed: 19.92. Those numbers are reproducible: a different total means a different seed, a different bounce rule, or a different particle count, not a different machine.
• The final average speed lands near 20, the middle of the 10 to 30 range you sampled from, and it equals the run mean (totalDistance / (Count * steps * dt)). Print both and compare them: they agree only because bouncing flips a sign and never rescales. If they diverge, Step is changing speed somewhere.
• bounds.Contains(p.Position) is true for every particle after every step.
• The pitfall demo prints (1.00,1.00) and then (2.00,2.00). If the first line already reads (2.00,2.00), you wrote the value back and lost the demonstration.

Hints: Vector Math & Simulation (Guided)