"The students will need to think outside the square and use their creative capabilities to find solutions," said Royal Society of New Zealand chief executive Andrew Cleland.
"At the end of the three days, each team will present its findings at a special presentation."
To be selected for Powering Potential, each student was required to submit an in-depth application and video which focused on their own science strengths or outlined how they had contributed to an area of science in their school or community.
The students were selected because they are serious about going on to study science at a tertiary level, and also have a passion and thirst for the world of science.
Dr Cleland said the calibre of the students that applied was excellent and some tough decisions had to be made by the selection panel to get the number down to 40.
Grandmaster of Freemasons New Zealand John Litton said they were "absolutely delighted" to be involved in Powering Potential.
"Education is a cornerstone of freemasonry. Our organisation is all about self- improvement and having the courage to make changes for the benefit of all."
All costs for the students, including social activities, are covered by the Royal Society of New Zealand and Freemasons New Zealand.