1. Why don't you go to the park together?

- Because I am too tired.

2. Why don't we go to the park together?
- Because I am too tired.

3. Why didn't you go to the park together?
- Because I was too tired.

4. Why didn't we go to the park together?
- Because I was too tired.
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Which dialogues are grammatical? Which ones are not? The patters are a bit difficult.

1and3 don't make sense. The others are fine.

All four dialogues are grammatical. However, there is a minor correction to be made in the choice of the word "patterns" in your last sentence. The correct word to use would be "dialogues" instead of "patterns". So the corrected sentence would be: "The dialogues are a bit difficult."