A person stands in the middle of a regular octogonal room with a flat mirror on one of the eight walls. When the person faces north-east, the person's reflection appears to face north-west. What direction must the person face in order to look directly into the mirror?
— submitted by Novalith
Think you have it? The answer is below.
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Answer: East or west — straight at the mirror wall (NE→NW means the mirror flips east/west, so its wall faces east or west)
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📖 The answer, explained
The trick here is remembering how mirrors actually flip things — not up and down, and not simply left and right either, but front to back along the line running straight into the glass. Whatever direction is perpendicular to the mirror gets reversed, while the direction running parallel to it stays the same. So when facing northeast turns into facing northwest, the shared piece is north — that's the axis lying flat against the mirror's surface and staying untouched. The part that flipped is the east/west component, which means that's the axis running straight through the glass. So the mirror itself must be mounted on a wall facing directly east or west, and to look straight into it, you'd need to turn and face that same direction — east or west — squarely, sending your gaze straight in and straight back with no angle to bend.
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