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Not sure if you can limit it directly in the UI, but you can limit it when saving the page. See this article: http://world.episerver.com/code/dannymurphy/contentarea-item-limiting/
Another option could be to create your own ContentAreaRenderer and do your magic there. I wrote a blog article about manipulating a single item but I think you could change how all items are rendered. http://www.kloojed.com/render-contentarea-items-with-ehm-spacing/
/Marcus
Have a look at Henriks blog post for an example of how to implement custom validation to do that:
http://henrikm.com/custom-episerver-property-validation/
Paul
Thank you, Paul - Henrik's solution works well enough for my purposes. I appreciate your help!
Is there a way to limit the number of blocks a user can insert into a block container? The design is only for 3 items, so I don't want my client to be adding more than that.