## How to create an extreme overhang with toy bricks

2019-03-14 07:04:04

By Ben Longstaff Your festive dinner is nearly at an end and just when you think you’re about to burst, out come the after-dinner mints. Instead of dicing with indigestion this year, why not try a spot of practical mathematics? Your challenge is to build a stack of mints on the edge of a table and see how far you can make the pile jut out without toppling. If you have already guzzled the mints, try it with dominoes or building blocks instead. OK, it’s hardly an extreme sport but you’ll be amazed at what is possible. Just ask computer scientist Mike Paterson at the University of Warwick in the UK. Earlier this year, he and his colleagues demolished a long-standing result in mathematics that relates how far the overhang can extend with a given number of blocks – and demonstrated some extraordinary structures on the way. It’s great news for anyone wanting to impress friends and family, or trying to arrange an unfeasibly large number of presents under the Christmas tree. The overhang puzzle has been doing the rounds in engineering and mathematical circles since the mid-19th century. Most people have tended to focus their attention on the simplest stacks, in which the blocks are simply piled one on top of the other, with each block sticking out slightly further than the one below. To achieve the maximum overhang, each block is placed as far out as is possible without it toppling off or being unbalanced by those above it. It turns out that to do this,