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 that mirrors don't actually swap left and right — they flip whatever direction points straight into the glass. So the real clue is hidden in what stayed the same between your facing and your reflection's facing. You faced north-east, and the reflection faced north-west. Notice the north part never changed — only east flipped to west. That tells you the mirror's flipping axis runs east-west, meaning the wall it hangs on is oriented along that same east-west line. To look dead-on into any mirror, you must face along its flipping axis, straight at the glass. Since that axis here is east-west, standing in the center and facing either east or west sends your gaze directly into the mirror, with no leftover north or south component to throw off the reflection.
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