Not debating the entire concept of whether homework is a good idea or not, but whether solving a problem without actually doing all the legwork to get there, counts as "doing one's homework."
Tiven brings home worksheets that have instructions like, "Help the bunny find the carrot. Draw a line connecting each square that contains a 3, 4, or 5." There is a grid of addition & subtraction problems. Rather than do all the problems & then find the 3s, 4s, and 5s, she does the first few, finds the pattern, and then only does the problems that help take her to the end. Last night she did 11 out of 42 problems, but she argued that she had done her homework because she found the line from the bunny to the carrot, and that's what the instructions said to do.
I remember arguing with my geometry professor in high school when I wouldn't show the details but got the answer correct anyway & he tried to mark me down. On tests, sure, I can understand why he'd want to see that I can actually do the work. But if I can compute the hypotenuse of a right triangle in my mind, why bother writing the formula & calculations out? It's just homework, which is supposed to enforce the learning done in the classroom, and I obviously had it down because I got good grades on the tests. Needless to say, I'm on Tiven's side in this one. I'm not a fan of "homework for homework's sake."