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File: StackingBlocks On the page about infinity we mention that there are things that go wrong if you rely on your intuition. This page describes one of them. You may also want to see the page where CantorVisitsHilbertsHotel, or the BallsInBarrels page. ********> width="40%" !! Introduction Take a block about the size of a paperback book. Or a hardback book, or a brick. It doesn't really matter. If you try this for real you might want to use dominoes, CD cases, or something similar. But start with a bunch of blocks. !! Taking the first step Now put the first block on a table with its edge lined up neatly. Push it gently out over the edge of the table, and get it as far out as you can. How far can it go? Most people guess, correctly, about half way. So far so good. ******** width="10%" ******** width="50%" !! Bit tricky, this ... Now put two blocks, one on top of the other. Push the top one out until it's halfway off the bottom one, then start to push the pair of them together out until they can't go any further. How far do they get? Well, the combined centre of gravity can't go further than the edge of the table, so the second block ends up a quarter of the way off the table. That means the top one is actually 3/4 off the table! !! How far can we go? The question now is this: If you're allowed any number of blocks, just how far can you get the top one hanging over the edge of the desk. The answer may surprise you. ********<