On a whole different scale to entering competitions, there are a number of institutions around the world which offer large cash prizes for solving big problems.
These may be global issues offered through Nesta.org.uk such as producing easy to use bacteria testing kits to combat bacterial resistance (with an eight million pound prize). Or mathematical challenges such as the seven Millennium Prize Problems that have stumped mathematicians for decades (each with a million dollar prize for the person who solves it). The X prize runs regular challenges to solve some of the biggest problems that are currently facing humanity.
There have been others in the past such as the James Randi Foundation which offered a million dollars for anyone that could prove paranormal abilities under agreed conditions.
As you can imagine some of these require teams of experts to partake with upfront cash investments. Others you only need use your mind, some time and out of the box thinking.
Sites to use
Millennium Prize Problems – 7 Maths problems with a $1,000,000 prize each.
Nesta Challenges – Solve some of the world’s most pressing problems.
X Prize – Foundation to achieve large goals. Millions of dollars of prizes.
James Randi Educational Foundation – $1,000,000 prize for evidence of paranormal abilities. Finished in 2015.
Paranormal Prizes – List of prizes for evidence of the paranormal.