Volume 55
, Issue 1

2019

Dear Readers, welcome to this year's first issue of Parabola!
In it, I am excited to bring you interesting and excellent articles, problems, and comics. Enjoy!

Are players of popular online games like Spider Solitaire justified in suspecting that some games are rigged? This article shows that random walks can be used to settle accusations of bias.

This article presents Adams' Circle, a 176-year old but yet little-known circle closely related to any triangle, and further presents new and beautiful geometrical research.

This article describes how to count the number of paths across an obstructed grid.
It turns out that this number of paths is fundamentally connected to the Inclusion-Exclusion Principle and Pascal's Triangle.

An odd comic about even numbers.

Q1583 Coins are placed in an $n\times n$ 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?

Q1571 Find positive integers $a,b,c$ such that $a \leq b \leq c$ and
\[
    \frac{1}{a}
  + \frac{1}{ab}
  + \frac{1}{abc}
  = \frac{5}{26}\,.
\]