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And even if you had such a tool, it's likely to be less effective than a writer, who will naturally use desirable variations of words during the process of writing.
As for how many keywords per page, I'll be slightly mischievous and say: a hundred? A thousand perhaps? How many is going to depend on what you write and how popular the theme of your page is. If you have a 500 word article, there are a substantial number of 2, 3, 4, 5 word etc. combinations that your page can theoretically target.
There are excellent tools out there that allow you to analyze the top XX search results for, among other things, keyword density.
In geneal, I usually stick with the average keyword density of the top 20 google result pages unless they ALL have extremely high # of backlinks (which is something to factor in)
[edited by: Receptional_Andy at 11:50 am (utc) on June 27, 2008]
[edit reason] Removed specifics as per charter [/edit]