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BrainteasersJane StreetSIG

Four jealous couples cannot cross with a two-seat boat

river-crossingimpossibilitystate-searchinvariant

Four married couples must cross a river. As usual, no wife may be on a bank or in the boat with another man unless her husband is present. Everyone can row, and there is no island to use as a staging post.

  1. With a boat that holds two people, can they all get across?
  2. With a boat that holds three people, can they, and in how few crossings?
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Look at any moment when there are husbands on both banks. What does the jealousy rule then say about where each wife must be? That observation makes the two-seat case collapse.

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