Daily Math Puzzle: 2026-07-05

Astronauts on a deep-space mission encounter an ancient alien beacon transmitting data about newly discovered star systems. Each system is assigned a unique 'Stellar Signature' based on its number of planets. They've deciphered a few examples: - System 'Andromeda Alpha' with 6 planets has a Stellar Signature of 4. - System 'Beta Centauri' with 10 planets has a Stellar Signature of 4. - System 'Gamma Draconis' with 12 planets has a Stellar Signature of 6. A new system, 'Delta Epsilon', has been found with 18 planets. Based on the alien pattern, what is its Stellar Signature?

During a magic show, the magician displays a clear cube that has a tiny red dot painted on the center of the top face and a tiny blue dot painted on the center of the bottom face (the two dots are on opposite faces). The other four faces are plain. He then performs two secret moves while the audience watches: first he rotates the cube 90° clockwise around a vertical axis (so the front face moves to the right), and then he rotates the cube 90° clockwise around a horizontal axis that runs left‑to‑right (so the top face moves toward the audience). After these two rotations, which two colored faces now share a common edge?

At the 'Wacky Whirlwind' ride, there's a circular platform with a radius of 5 meters. A smaller, circular safety zone is marked in the exact center of this platform, with a radius of 1 meter. A maintenance worker needs to walk a specific path: starting from a point on the *outer edge* of the main platform, straight to a point on the *outer edge* of the safety zone. From there, they walk straight across the *diameter* of the safety zone. Finally, from the other side of the safety zone, they walk straight to another point on the *outer edge* of the main platform. To ensure minimal effort, what is the *shortest possible total distance* the worker could walk for this entire path?