Which of the following sentences is

grammatically correct?

1. Since we can get another one, it didn't matter anyways that we can't find it.
2. She felt badly that she arrived so late.
3. Of all the students in the class,he
asked permission most politely.
4. He sure was real smart to figure that out.

Which of the following sentences is
grammatically correct?

1. Since we can get another one, it didn't matter anyways that we can't find it.
problem with consistency of verb tenses -- present and past tenses are mixed up

2. She felt badly that she arrived so late.
"badly" is an adverb -- did she have trouble feeling?

3. Of all the students in the class, he asked permission most politely.
looks good

4. He sure was real smart to figure that out.
"real" is an adjective -- you need an adverb to modify the succeeding adjective, "smart"

=)

1. Since we can get another one, it didn't matter anyways that we can't find it.
problem with consistency of verb tenses -- present and past tenses are mixed up

Anyways is not a standard English word. I think your verb tenses are correct.