Volume 55


Dear Readers, welcome to this issue of Parabola!
In it, I am excited to bring you interesting articles, addictive problems, and pretty punny comics. Enjoy!

Living with others, you might sometimes have to wait to use the bathroom. The fewer bathrooms or more people, the longer you'd have to wait. But can we mathematically calculate how long we can expect to wait every day? One approach is to use so-called Markov chains.

The problem of the aircraft squadron is that of determining how far some aircraft from a squadron can fly if the aircraft are able to share fuel, and which fuel-sharing strategy might work best?

Ancient Babylonians used Pythagorean triples to conduct real-life calculations but, although that was nearly 4000 years ago, these triples have not been greatly studied.

Laugh and wince at these punny comics.

Q1591 For \(f(x)=x^4+2x^3-7x^2+11\), find a line which is tangent to the graph $y=f(x)$ twice.

Q1583 Coins are placed in an array, alternately heads up and tails up. At each move, you are allowed to turn over all coins that form one connected region. How can you get all the coins heads up in the minimum possible number of moves?