The annual competition, which is sponsored by Mourant Ozannes and staged at St James, saw pupils from Grammar, Elizabeth College and La Mare de Carteret High compete for the Raymond Falla Memorial Trophies.
Each three-person team had a fixed amount of time in which to present their case, before answering questions about their chosen topic from the judging panel, headed by Mourant Ozannes' Jessica Roland.
Grammar's senior team of chairman Hannah Ogier, speaker Pieter Durman and vote of thanks Lauren Guille, all 16, won the overall prize with their topic 'How to Solve a Problem Like Mary'.
'We were looking at the nativity and how people cope with not getting the parts they wanted, and then more widely at how people cope with disappointment later in life,' said Pieter.
Hannah said: 'I was so nervous beforehand, but taking part gives you a real feeling of achievement.'
The team will now take part in the district final in Taunton on Saturday 11 March, where they will compete for a place in the national final.
And they said sharing the stage with new teams would be 'a great experience'.
'Part of our speech was that success is never final, so we will have plenty to work on before then,' Lauren added.
Elizabeth College pupils Jack Cummins, 14, Isaac Powers, 14, and Alex Varley, 15, won the intermediate class for Years 10 and 11.
They used a fictional supervillain to personify many people's pessimistic outlook for the year ahead.
