My first try (omitting chain of thought for brevity):
When you remove the cup and the mirror, you will see tails. Here's the breakdown:
Setup: The coin is inside an upside-down cup on a glass table. The cup blocks direct view of the coin from above and below (assuming the cup's base is opaque).
Mirror Observation: A mirror is slid under the glass table, reflecting the underside of the coin (the side touching the table). If the mirror shows heads, this means the underside of the coin is heads.
Coin Orientation: A coin has two sides: heads and tails. If the underside (facing the table) is heads, the top side (facing away from the table) must be tails.
Result: Removing the cup reveals the coin on the table. Since the top side was tails all along, you will see tails.
Key Insight: The mirror reveals the hidden underside of the coin, but the top side (visible after removing the cup) is its opposite. The mirror’s reflection does not alter the physical orientation of the coin’s sides—it simply reflects the existing state.
Answer: Tails.
Answer:
You will see the same side of the coin that you saw in the mirror — heads .
Why?
The glass table is transparent , so when you look at the coin from below (using a mirror), you're seeing the top side of the coin (the side currently facing up).
Mirrors reverse front-to-back , not left-to-right. So the image is flipped in depth, but the orientation of the coin (heads or tails) remains clear.
Since the coin hasn't moved during this process, removing the cup and mirror will reveal the exact same face of the coin that was visible via the mirror — which was heads.
While technically true, one could argue that because they described sliding a mirror underneath the table, that they did this in order to be able to see from that particular angle, so the implication for any reasonable answer would be that are looking down at the table.
The way the question is phrased, I'm definitely in the "ok, what's the trick, what do you want to hear" mode. I'm not surprised LLMs answer in a weird way with extra details like "this is how mirrors work, is this what you're confused about?"
Manus just answered this correctly for me in one crack:
Me:
I put a coin in a cup and slam it upside-down on a glass table. I can't see the coin because the cup is over it. I slide a mirror under the table and see heads. What will I see if I take the cup (and the mirror) away?
Manus:
This is a classic riddle! Let's think it through. You placed a coin in a cup, turned it upside down on a glass table, and then slid a mirror underneath the table. Looking into the mirror from below, you saw 'heads'. Since the mirror reflects the side of the coin facing downwards through the glass table, the 'heads' side must be facing down. Therefore, the side facing up, hidden inside the cup, must be 'tails'. When you remove the cup, you will see the side facing up, which is tails.
