Last fall a YouTube channel titled Life's Biggest Questions tackled the question of "how tall can a LEGO tower get?" The video explains the math that was used by researchers at The Open University to figure how tall a LEGO tower would get before the blocks collapsed under their own weight. Of course, the mathematical answer assumes that the tower wouldn't topple over before reaching it's maximum height. So you then have to consider the overall stability of the structure instead of just weight-bearing capability of the structure. Watch the video to learn more, it's quite enjoyable.
Applications for Education
The question of "how tall can a LEGO tower get?" is a fun prompt for diving into discussions about math and physics. Before showing students the video or the article mentioned above, I'd have them make guesses as to the answer then write out lists of the variables that they can think of that would influence how tall the tower could get. Then after they watch the video I'd have a little classroom contest to see who can build the tallest tower with the LEGOs available in my classroom.