1. Some like summer and others like winter.

2. Some like summer and the others like winter.

3. Some like summer and another likes winter.

4. Some like summer and the other likes winter
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#1 and #2 are right? Right? What about Sentence 3 and Sentence 4? Are they all grammatical?

They are all four compound sentences, so there should be a comma after "summer"

#1 is probably the best.
#2 implies that there is a specific group of people under discussion.

#3 and #4 suffer from a mismatch between plural and singular.