Question 9
Let $n$ be a positive integer. A flea on the real line makes $n$ jumps of lengths $1,2,3,\ldots,n$. It may choose the order of the lengths and whether each jump goes right or left.
a. Prove that for $n=2012$ it can finish at its starting point.
b. Prove that for $n=2013$ this is impossible.
c. In general, for which $n$ can it return to its starting point?
a. Prove that for $n=2012$ it can finish at its starting point.
b. Prove that for $n=2013$ this is impossible.
c. In general, for which $n$ can it return to its starting point?