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When the farmer returns to the original side, he has the choice of taking either the wolf or the cabbage across next. If he takes the wolf across, he would have to return to get the cabbage, resulting in the wolf eating the goat. If he takes the cabbage across second, he will need to return to get the wolf, resulting in the cabbage being eaten ...
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Phases of play are parts of a chess problem which happen, as it were, concurrently rather than consecutively. Each problem has at least one phase: the post-key play or actual play ; that is, the play after the key (the first move which leads to the problem's stipulation ("mate in two" or similar) being fulfilled).
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The farmer can't take two items across the river at once. The conditions of the puzzle say "in crossing the river by boat, the farmer could carry only himself and a single one of his purchases". As for citations, there are plenty in the References section, and the Occurrence and variations section describes the origins of the puzzle.
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