1. They moved in yesterday.

2. They moved out the day before yesterday.
3. They moved into yesterday.

4. They moved in the apartment yesterday evening.
5. They moved into the apartment yesterday evening.
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Are they all grammatical except Sentence 3?

6. He is alone at the apartment.
7. He is alone in the apartment.

8. She is alone at the house.
9. She is alone in the house.

10. They are alone at the place.
11. They are alone in the place.

(Are the pairs all correct? Are 'at' and 'in' interchangable?)

3 is incorrect.

The word "in" in these sentences generally means "inside" while "at" could mean either "inside" or "near."

Let's analyze each sentence individually to determine their grammaticality:

1. They moved in yesterday. ➡ This sentence is grammatically correct. "Moved in" refers to the action of someone settling into a new place.

2. They moved out the day before yesterday. ➡ This sentence is also grammatically correct. "Moved out" indicates the action of someone leaving or vacating a place.

3. They moved into yesterday. ➡ This sentence is not grammatically correct. The correct phrasing should be "They moved in yesterday."

4. They moved in the apartment yesterday evening. ➡ This sentence is grammatically incorrect. The correct preposition to use with "move in" is "into." The correct phrasing would be "They moved into the apartment yesterday evening."

5. They moved into the apartment yesterday evening. ➡ This sentence is grammatically correct. "Moved into" represents the action of someone settling into a specific location, in this case, the apartment.

Now, let's move on to the second set of sentences:

6. He is alone at the apartment. ➡ This sentence is grammatically correct. "At" typically refers to a general location or point, suggesting proximity to a place but not necessarily inside.

7. He is alone in the apartment. ➡ This sentence is also grammatically correct. "In" indicates being inside a specific location, in this case, the apartment.

8. She is alone at the house. ➡ This sentence is grammatically correct. Similar to sentence 6, "at" implies proximity to a location but not necessarily inside.

9. She is alone in the house. ➡ This sentence is also grammatically correct. "In" denotes being inside a specific place, which is the house in this case.

10. They are alone at the place. ➡ This sentence is grammatically correct. The use of "at" suggests proximity to a particular location but not necessarily inside it.

11. They are alone in the place. ➡ This sentence is also grammatically correct. "In" implies being inside a specific location.

Regarding the interchangeability of "at" and "in," while they can sometimes be used interchangeably when expressing location, there are subtle differences in meaning. "At" typically denotes a more general or approximate location, while "in" describes being inside a specific place. The choice between the two prepositions depends on the intended meaning and context.