Can anyone tell me how to display a set of widgets in random order in a sidebar?

Specifically, every time someone visits a page/post they haven't visited before, I'd like them to see the widgets in a different order. But there are a few widgets I'd like to be "anchored" in place. So, for example, I'd like them to see:

Page/post 1 left sidebar:
widget 1
widget 2
widget 3
widget 4
widget 5
widget 6

Page/post 2 left sidebar:
widget 1
widget 2
widget 3
widget 6
widget 5
widget 4

Page/post 3 left sidebar:
widget 1
widget 2
widget 3
widget 5
widget 6
widget 4

Please note that I plan to use way more than 6 widgets, so I'll need some sort of randomize/shuffle function rather than hard-coding the widget order for each page. Also, it's okay (perhaps even preferable) if the widgets are displayed in a different order every time someone refreshes a page/post.

I looked for plug-ins and solutions elsewhere on the web, but I couldn't find anything.

Thanks in advance for any help anyone might provide!

You might be able to use widget logic and put a bunch of widgets in the sidebar then put a php random test in each one.

However, I don't think this is a very good idea. People are use to looking to the sidebar for constant information, links etc. I'm not sure I would revisit a site where the number of widgets and the actual widgets changed in a random order. It would be too confusing and distracting.

Come to think of it, you're probably right. Thanks for your reply.