Here’s the challenge: each frog sits on a vertex of a cube, leaving exactly one corner empty. A move is only allowed if a frog jumps over another frog—landing at the point that is the reflection of its position across the jumped frog. In math terms: if frog A jumps over frog B, its new position is 👉 A′ = 2B − A This is a geometric reflection (or a 180° rotation around B). Sounds simple… but here’s the twist: Can you create a sequence of these reflections so that any frog lands exactly on the one empty vertex? ⸻ 💡 What’s really happening under the hood: * Each corner of the cube can be represented as coordinates like (0,1) in 3D → binary vectors in {0,1}³ * Each jump preserves a hidden invariant (a property that doesn’t change), related to parity and vector sums * The system behaves like a constrained transformation group over discrete space This is where geometry meets algebra—and intuition often fails. ⸻ 🧠 Try it before reading the comments: Is it possible… or is there a hi...