Question 2
Genji the ninja is to jump along the real axis, starting at the point $0$. In doing so, he alternates between the following two types of jumps, his first jump being type 1.
**Type 1:** Genji jumps from the current position $x$ to a point $y$ in the set
$$
\{x, x+1, x+2, x+3, x+4, x+5, x+6\}.
$$
**Type 2:** Genji jumps from the current position $y$ to $(\sqrt{2}-3)y$.
Let $a$ and $b$ be integers. Prove that there exists a finite sequence of jumps that allows Genji to land on the point $a+b\sqrt{2}$.
**Type 1:** Genji jumps from the current position $x$ to a point $y$ in the set
$$
\{x, x+1, x+2, x+3, x+4, x+5, x+6\}.
$$
**Type 2:** Genji jumps from the current position $y$ to $(\sqrt{2}-3)y$.
Let $a$ and $b$ be integers. Prove that there exists a finite sequence of jumps that allows Genji to land on the point $a+b\sqrt{2}$.