= Solution
Write $(a,b,c)$ for holdings of cash, the <stock> and the <European put option>, and let $\gamma=-V_0$ be initial <consumption>. At the given price, $a=-10b-c-\gamma$, and the three terminal payoffs, in descending order of the <stock> price, are
$$
5b-c-\gamma,\qquad2b-c-\gamma,\qquad c-b-\gamma.
$$
Nonnegative terminal payoffs require $c+\gamma\leq2b$ and $c-\gamma\geq b$. Together with $\gamma\geq0$, these imply $b\geq2\gamma\geq0$. If $b=0$ they force $\gamma=c=a=0$, which is not an <arbitrage>. If $b>0$, the highest-state payoff is at least $3b>0$, so every such choice is an <arbitrage>. Consequently the complete set is
$$
\boxed{(a,b,c)=(-10b-c-\gamma,b,c),\quad b>0,\quad0\leq\gamma\leq b/2,\quad b+\gamma\leq c\leq2b-\gamma.}
$$
The <pure-investment arbitrages> are exactly the choices $\gamma=0$:
$$
\boxed{(a,b,c)=(-10b-c,b,c),\quad b>0,\quad b\leq c\leq2b.}
$$
For example, $(a,b,c)=(-11,1,1)$ costs zero and pays $(4,1,0)$.
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