At the node with stock price thirty, both possible next prices exceed thirty-three, the value of thirty invested at gross rate . Take no position at time zero. If the first move is good, borrow thirty at time one and buy one share; if it is bad, do nothing. At time two sell the share for forty-five or thirty-six and repay thirty-three, leaving twelve or three. The strategy has zero initial cost, no possible loss, and positive profit on the good first move, so it is an arbitrage.
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