A Puzzle A Day: 2026-05-01

An experimental deep-space probe, shaped like a perfect cube, is observed tumbling rapidly in orbit around a newly discovered exoplanet. As it spins, a sophisticated orbital telescope captures a fleeting, high-resolution snapshot. In this specific image, the probe's silhouette against the blackness of space appears as a perfect, symmetrical hexagon. Assuming no self-occlusion from overlapping parts of the probe (it's a solid cube), how many of the cube's 6 faces are guaranteed to be visible to the telescope in this precise snapshot?
Correct: 6
When a perfect cube is viewed from a precise angle, specifically along one of its body diagonals (the line connecting two opposite corners), its projection onto a 2D plane forms a perfect regular hexagon. In this unique orientation, the observer is looking directly towards two opposite vertices of the cube. The three faces that meet at the closest vertex are clearly visible. However, due to the specific geometry of viewing along a body diagonal, the three faces that meet at the *farthest* vertex are also partially visible, appearing 'around' the edges formed by the intermediate vertices. Therefore, all six faces of the cube contribute to the visual image and are considered visible from this particular perspective.
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