The 15th annual European Union Contest for Young Scientists involved 25 ground-breaking projects on everything from how to walk through puddles without getting your trousers dirty to how to determine the speed of light from the movements of Jupiter.
But one problem common to most of the 117 scientists was less easy to solve than their mind-blowing conundrums - funding.
Jana Ivanidze, 19, from Munich, jointly won first prize for discoveries on cell communication that will enable a greater understanding of hormonal reactions and the basis of human life. It took five years working outside school hours to complete the study.
"The University of Munich laughed at me when I approached them at the age of 14," said Miss Ivanidze. "I phoned a professor every day for six months asking to use the university's laboratory until he finally gave up.
"I was not encouraged at school, but I am very driven. You cannot wait for someone to offer you an opportunity."
Most participants at the contest were self-starters who had also triumphed against the odds. Uwe Treske, an 18-year-old German school leaver, reproduced a microscope which usually costs about pound;1 million for pound;25. Filaments served as a microscope tip and a pile of towels dampened any undesirable vibrations. He used a standard PC sound card for the digitisation of the measuring signal.
In Denmark Thomas Rasmussen turned his parents' basement into a smelly brewery and used old hospital equipment to experiment with fermentation. By varying the temperature at different stages he devised a method to produce beer ten times more quickly than is usual in breweries.
Nienke Boone and Sylvie Ackaert from Belgium are dreading any unforeseen side-effects of a homemade shampoo which they tested on 11 family members.
And Laszlo Nagy, who is passionate about fungi, spent months touring 1,100 localities in the Great Hungarian Plain in order to find two new species.
Like most contestants Redslaw Poleski only heard of the contest by chance from contacts outside school. He produced a formula to prove there is life on other planets after attending an astronomical camp run by a Polish charity.
Most students felt their schools had been unsupportive. Representatives from Switzerland, for example, said far more emphasis is put on languages than science in school.
But the British entrants were an exception. All three got pound;400 bursaries from the Nuffield foundation for their three-month projects.
Alex Morris, 18, joined researchers at Sheffield University working to increase the memory of computer hard drives. Tapton school in East Yorkshire arranged his bursary and entry to the national science contest that precedes the EU competition. Alex has also attended the National Academy for Gifted and Talented Youth. The British Association, which is funded by the Government, organised the national contest.
Amy Sanders, young person's programme officer at BA, said: "Other countries seem less organised at school level than in Britain. Nonetheless, we still need to encourage more creative science rather than a dry curriculum."
The difficulty of promoting science in school was a recurring theme at the Budapest conference. Experts from America and Europe reported that fewer people than ever are going into science.
Sir Harry Kroto, joint winner of the 1996 Nobel Prize for chemistry, said:
"Science offered the best future when I was young but now other professions like law are much better paid.
"When I was a kid I made my own radio whereas nowadays it would cost half the price to buy one. Science has become so submerged in our culture that people no longer appreciate it. As a subject in school it is often perceived to be too difficult."
Ivar Giaver, winner of the 1973 Nobel Prize for physics, added: "You can never go back and learn science later in life, but start young and the world is open to you."
Achilleas Mitsos, director general of research at the European Commission, told The TES that a change of image, not official directives, were the answer.
"We must try to change the image of science and the stereotypes of old men observing work in backroom laboratories. We need new ways of teaching and approaching science. Youth and science are the future. If we cannot find a way to make scientific careers attractive for young people we have failed."
The commission's Sixth Framework Programme funded the science contest and nine prizes totalling e28,000. It is building new programmes for teachers and wants each member state to spend 3 per cent of its GDP on research and development by 2010.