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[url= http://www.bbc.co.uk/news/magazine-20578627 ]2.17 miles[/url]
Radio 4 did a piece on this the other week...375000 blocks, took 1/2 ton to crush a 4x4 block.
if (using old style lego) ie the little blocks that were 4 dots by two dots on the top you build an square outer cylinder with a tiny 1 hole at the bottom - e.g. big enough to stick the fuse part of a banger out of, and then build a square insert of the correct size, drop on top of banger and retire you should be able to get the insert up to the height of a two storey house roof.
Theoretical possible, but not physically, 3-4 meters is the max physically given in the article, using only 2x2 bricks going straight up.
They built a house out of Lego in a vineyard in Dorking a few years ago, it was quite impressive