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. A mirror doesn't swap up and down, and it doesn't swap left and right the way people casually assume — it flips whatever axis is perpendicular to its surface, the front-to-back one. So when facing north-east becomes facing north-west in reflection, the north part of that direction stayed put while the east part flipped to west. That's your clue: the mirror is reversing east-west, which means the wall it hangs on runs along the north-south line, facing east or west. Once you see that, the geometry stops mattering — the octagon, the walls, the room shape are all misdirection dressing up a simple reflection-axis question. To look straight into the mirror, you just face the same direction the wall faces: east or west, dead on, no angle to flip at all.
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