Question 7
A flea jumps over whole points on the number line. In his first move he jumps from point $0$ and lands at point $1$. Then, if in one movement the flea jumped from point $a$ and landed on point $b$, in the next movement it jumps from point $b$ and falls on one of the points $b + (b - a) - 1$, $b + (b - a)$, $b + (b - a) + 1$.
Show that if the flea has fallen twice on the point $n$, for $n$ positive integer, then it must have made at least $t$ movements, where $t$ is the smallest integer greater than or equal to $2\sqrt{n}$.
Show that if the flea has fallen twice on the point $n$, for $n$ positive integer, then it must have made at least $t$ movements, where $t$ is the smallest integer greater than or equal to $2\sqrt{n}$.