Page 145, problem 581, problem diagram
Page 146, problem 581, solution diagram
Throwing in a stone with 1 is a tesuji to reduce White's liberties. Black captures three stones after 3.
Skelley: I think White can make a seki by connecting at 2 after Black 1; the sequence up to 6 results in a seki. Unfortunately we don't know what will happen if Black cuts at x since there is no information on the board position. If the rest of the board is empty I am assuming that White can escape with those three stones there...
Andre Engels: Since the claim is that black lives, not that black has two eyes, I don't see why this would be an error in the book.
Skelley: If white can make the seki she saves a whole bunch of stones and prevents black from making any territory in the corner. To me that seem like a much better way to play for white.
ferdi: Andre is right. But even in a whole board context, the given solution is fine:"4" and "5" show the continuation from "2" (8 connects). White has two points less here, but since the cut at "a" isn't a threat anymore, at least this shouldn't be worse than the seki.