Andrew, these solutions are not guaranteeing the minimum. They are heuristical. Using one extra trunk is their normal behaviour. Look at the thesis mentioned earlier. I tried to find the mathematically perfect solution, but it takes hours or years, to execute. There has not been much conversation about this quiz. I think the reason was Ilmari's and Adam's excellent (and early) contributions. It was impossible to improve on them. Christer -- Posted via http://www.ruby-forum.com/.