1. On the one hand they want to go abroad, but on the other hand they want to save more money.

Question

2. On the one hand they like playing ping-pong, but on the other hand they want to go back home early.

3. On the one hand they want to play soccer, but on the other hand they want to take a rest in the shade.

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Are they all grammatical? Would you correct errors?

Answer 1

I'd put a comma after each instance of "hand," but all three sentences are grammatically correct.

I'd also be more likely to put a semicolon where you have the comma in the middle of each sentence -- and then I'd omit "but."