Tomorrow is Pi Day – March 14 – the annual excuse for the mathematical community to circulate puns about buns. I mean to honour pi, the ratio of a circle’s circumference to its diameter, which to two decimal places is 3.14, hence 3/14, as the Americans write tomorrow’s date.
In recent years Pi Day has gone from a geeky American eccentricity to a global celebration of maths, and I’m getting my r’s in a day early with two puzzles from the brilliant minds at Brilliant.org. (That’s r for radius, obvs.)
The first is all about pie, in all its homonymic glory. Pictured below are three identical boxes packed with pies. Which box contains the most pie?
You can assume that all pies are exactly the same height.
The next question is about a virus. One hundred computers are connected in a 10×10 network grid, as below. At the start exactly nine of them are infected with a virus. The virus spreads like this: if any computer is directly connected to at least 2 infected neighbours, it will also become infected.
Will the virus infect all 100 computers?
The image shows a possible example of the initial infection. You can try to fill it in to see if ultimately the network will consist of 100 orange dots. But the question is not asking what happens to this example. I want to know what will happen given any initial configuration of infected computers.
It’s a lovely question – or rather, the solution is lovely. (And there is a connection to pi, but not an obvious one). Have a think, and then submit your answers to both questions here.
Which box contains the most pie?
A) A has the most pie
B) B has the most pie
C) C has the most pie
D) A,B and C have equal amounts of pie
Will the virus affect all 100 computers?
A) Yes, the virus will always affect all 100 computers
B) It depends on which nine are infected at the start
C) No, the virus will never infect all 100 computers
Feel free to reply to this blog with your answers.