On May 22nd 2009 the English Premier league had one more match day ahead, with West Bromwich Albion at the bottom of the league and Manchester United at the top, sure to remain there. Taking up a challenge from a BBC radio programme, David Spiegelhalterand Yin-Lam Ng used their statistical finesse to predict the outcome of the last matches — and they were 90% correct. Find out how they did it.
Here's an argument to show why there is no convex and homogeneous two-dimensional shape with one stable and one unstable point of equilibrium.
\textbf{Step 1} Let $k$ be either 3, 4, 5, or 6. \textbf{Step 2} Set $c := \frac{k-2}{2} = \frac{1}{n_1}+\frac{1}{n_2}+...+\frac{1}{n_k}.$ \textbf{Step 3} Set $n$ to be the biggest whole number less than or equal to $\frac{c}{k}$. Note that not all $n_i$ can be bigger than $n$, for otherwise $$\frac{1}{n_1}+\frac{1}{n_2}+...+\frac{1}{n_k} < c.$$ \textbf{Step 4} Suppose $n_1
Don't blow a fuse with this one
