= Solution
The stock tree has $S_0=5$, first-period values $6,4$, and terminal successors $7,5$ from $6$ and $5,3$ from $4$. When $r=1/6$, the risk-free growth factor is $R=7/6$. At the upper time-one node, investing $6$ in the risk-free asset produces $7$ at time two, while one share bought for $6$ produces only $7$ or $5$.
Use the following predictable <self-financing portfolio>. Hold nothing initially. If $S_1=6$, short one share and invest the proceeds $6$ in the risk-free asset; if $S_1=4$, continue to hold nothing. Its terminal payoff is
$$
7-S_2=
\begin{cases}
0,&S_2=7,\\
2,&S_2=5
\end{cases}
$$
on the upper branch, and zero on the lower branch. It costs zero, is never negative, and is positive with positive probability, so it is an <arbitrage>.
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