I read your question and the comments. With respect to all of the commenters who all left excellent comments from my point of view, I think there is a missing element in these considerations. Small, but important.
Your News and Archives pages will have more than one full article each and I assume other things too. It will not be an exact copy of your article in that respect. However, you still have the same problem. Sorta. As well, from the Article and Archive Article pages, I am sure that an article will age from one location to the other and so that would not be an issue.
So between /article and /archive I do not see a problem. But on the News and Archives pages, I do. Somewhat.
Here is what I am thinking.
I would not post the entire article on the News and Archives pages, but I like what you want to do, so I would suggest perhaps a larger portion of the article than just a snippet. Just for an example, if possible, perhaps half or a third of the article. I do not know what options your blog software gives you, or even if you can write code to help manage the appearance of your blog, but I would (from a programming perspective) take the first x number of characters from each article and make them available on your News and Archives pages. Assuming that most articles are at least 300 words, you should be able to take a good chunk of the article, something on the order of 1/3rd or 1/2 and post it with safety. As much as I do not like the read more links, perhaps that would be a good idea.
If this is not possible or is not an option you want, then I think you may have little choice but to no index the News and Archives pages unless these pages change rapidly. If this is the case, then you may not have a worry. If these pages change rapidly enough, then I assume that Google would mark these pages as having duplicate content. If you do no index these pages, then I would make sure there is a sitemap to make sure that your archived articles get indexed and that when an article moves from /article to /archives, that a 301 redirect handles this move for you.
Just some simple thoughts on the matter. You appear to have a nice scenario in mind. The question is, what is the best way to handle it. It may be that your setup will work fine without modification and you will not see any issues. But to know that for sure, you will have to try it. If you want to be sure there is not a problem, then I would suggest a sitemap and no index the News and Archives pages.