\question
A rod of length 1 is thrown at random
onto a floor tiled in squares of side 1.
What is the probability that the rod will fall
wholly within 1 square?
\question
Show that the number of ways of making up $n$ pence
from 1p, 2p and 5p pieces
is the nearest integer to $\frac{(n+4)^2}{20}$.
\question
For which positive real numbers $x$ does the sequence
\[
x,\; x^x,\; x^{x^x},\; \dots
\]
converge?
\question
Are there a finite or infinite number of numbers $n$
with the property that when the digits of $n$
are written in reverse order,
the result is equal to $3n$?