1. Would you give me a hand with the dishes?
2. Would you give me a hand to do the dishes?
3. Would you give me a hand doing the dishes?
(Are they all grammatical and do they have the same meaning?)
4. Would you give me help with the dishes?
5. Would you give me a help with the dishes?
6. Would you give me some help with the dishes?
(Does #1 mean #4 or #6? #5 is not correct, is it?)
I would use 1, 3, and 6. The others are awkward or incorrect.
4 could easily be changed for common use:
Would you help me with the dishes?
1. "Would you give me a hand with the dishes?" - This sentence is grammatically correct and commonly used. It means that you are asking someone to help you with the task of washing the dishes.
2. "Would you give me a hand to do the dishes?" - This sentence is also grammatically correct but less commonly used. It means the same as the first sentence - you are asking for someone's help with doing the dishes.
3. "Would you give me a hand doing the dishes?" - This sentence is grammatically correct and has the same meaning as the previous two sentences. It simply rearranges the words to emphasize the activity of doing the dishes.
So, yes, all three sentences (1, 2, and 3) are grammatically correct and have the same meaning.
4. "Would you give me help with the dishes?" - This sentence is grammatically correct, but it sounds a bit less natural than the previous three sentences. It means the same as the first three sentences, expressing a request for assistance with the dishes.
5. "Would you give me a help with the dishes?" - This sentence is not grammatically correct. In English, we typically use "some" before the noun "help" to indicate an indefinite amount of assistance, as shown in sentence 6.
6. "Would you give me some help with the dishes?" - This sentence is grammatically correct and has a similar meaning to sentences 1, 2, and 3. It emphasizes that you are asking for a certain amount of help, indicating that you may not need full assistance but just some support.
So, to answer your last question, sentence #1 means the same as #4 and #6. Sentence #5 is not correct as written, but using "some" in sentence #6 corrects the error.