I really liked having answers in the book (North America) - children I teach here are often really surprised, and can't believe we wouldn't have just cheated. But it was a totally different attitude to homework - here they see it as something the teacher makes them do, that they have to get finished, and preferably get the right answer, to get the ticks. For us, it was a way of checking that we understood the topic - if you weren't getting them right, you knew there was something wrong that you'd better sort out before going on to anything new, and because you were going to need to be able to do those questions for an upcoming exam. It was very much seen as our responsibility, not the teachers'. If you knew that you knew the work, you didn't have to do it, either. Or if you'd been assigned just the odd numbered problems, for example, and were getting them wrong, then you knew you'd better try the even ones as well until you got to the point where you were doing it successfully. That was what mattered more than anything else - knowing for yourself that you were at the point where you understood it well enough for exams/future work, and whether you needed help on it from the teacher. We all knew that there'd be no point just copying the answers from the book, since that wasn't the reason for doing homework. In fact, the teacher rarely ever took in the books or corrected it; the exams spoke for themselves. She might have wandered around looking at what had been done, to see how people were getting on with it, whether any common problems cropped up, etc., but that was it. I quite liked that sense of responsibility on the pupils to master something, to do as much or as little as they felt they needed to be able to do it.
But we were an advanced set, and it was quite a competitive school and we all wanted to do well on exams, which I'm sure made a difference.
I hate books that don't have answers, though, as it removes that responsibility from the children.