I think it's very important the Answerers disclose the method in getting the answer. Stack Exchange aims to provide helpful Q&A answers, and if future readers come for help and find your question, they are not going to understand your question.

It's sort-of like offering a kid help with his math homework, and then just giving him the answer. He learns absolutely nothing in the process.

It's a very important aspect to explain how you got your answer. If you don't it's usually a "guess". You know an answer is great when in clearly explains how to get to the correct solution.

May I ask why you'd even want to keep the method secret, even after the answer has been figured out?

I think it's very important the Answerers disclose the method in getting the answer. Stack Exchange aims to provide helpful Q&A answers, and if future readers come for help and find your question, they are not going to understand your question.

It's sort-of like offering a kid help with his math homework, and then just giving him the answer. He learns absolutely nothing in the process.

It's a very important aspect to explain how you got your answer. If you don't it's usually a "guess". You know an answer is great when in clearly explains how to get to the correct solution.

Wanting to continue suspense is not a good reason to withhold answers. If a user wishes to figure it out themselves they will. At the very most, place the method in a spoiler. It's great you want to encourage those that DO want to try, but you shouldn't prevent people who want to know the answer (whether trying or not), from seeing the solution in all it's glory. It would be highly unfair.