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Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
Generating electricity without the use of fossil fuels is not just an engineering and industrial challenge, it is also a huge mathematical challenge.
In this podcast author Coralie Colmez shares insights into her novel The irrational diary of Clara Valentine.
We talk to early career mathematicians who spent some of their summer holiday solving problems posed by industry — such as how to blend a perfect smoothie!
Don't like plant-based meat alternatives, but want to spare animals and the environment? There's hope on the horizon, aided by a good helping of maths.
Inverse problems are mathematical detective problems. They can help solve crimes, are used in medical imaging, and much more.
The unstated assumptions are not that everyone in the room is good at logic and that the person who makes the announcement is telling the truth, but that these two facts are common knowledge (see http://en.wikipedia.org/wiki/Common_knowledge_%28logic%29). The mere facts themselves don't lead to the solution, since all assumptions of the form "(everyone thinks that)*k everyone in the room is good at logic" for k from 0 to n-2 and "(everyone believes that)*k the person who makes the announcement is telling the truth" for k from 0 to n-1 are used at some point in the deduction.