A colleague recently showed me this amazing video. Were you familiar with this manifestation of Pi in nature?
In case you are interested, 3Blue1Brown uploaded a demonstration of this as a subsequent video on YouTube. How about trying to prove this by yourself?
There are N bottles, from which one contains a lethal poison that would kill whoever drinks from it in exactly 1 week.
What is the minimum number of people you need in order to determine which bottle contains the poison? You have just one week to find out which bottle it is.
A possible solution would be to use N people. Make each person drink from a different bottle and whoever dies after a week will tell us which bottle is poisoned. Can you do better?
Here I wrote a C++ code that will tell you the minimum number of people you need for any given number of bottles. Try to get the correct answer for N bottles and test your answer with the code. As a last resort you can reverse engineer my code to get the answer.
How long does it take for a physicist to tell you what time it is? Try first defining what the concept of time it self means.
Professor Brian Cox and Harry Hill talk about time:
How many pieces can you fit into a chess board?
The rules are:
I was able to fit 8 of each:
Can you do better?