Question 14
Farmer Tom must take a wolf, a sheep and a cabbage across a river. The boat can carry Tom and at most one of the three. Without Tom, a wolf left with the sheep eats it, and the sheep left with the cabbage eats it. Answer the following to find a route using the fewest crossings.
1. Which two of the three may safely be left together?
2. Which should Tom carry on his first outward trip?
3. Suppose on outward trip 1 Tom carries the sheep across, leaves it there and returns; on outward trip 2 he carries the wolf across. What should he carry back on return 2, and carry out on outward trip 3?
4. How many ways are there to transport all three across?
Editorial convention: part 4 counts shortest routes; distinguish the source’s outward-trip numbering from one-way crossings. Answer all four parts.
1. Which two of the three may safely be left together?
2. Which should Tom carry on his first outward trip?
3. Suppose on outward trip 1 Tom carries the sheep across, leaves it there and returns; on outward trip 2 he carries the wolf across. What should he carry back on return 2, and carry out on outward trip 3?
4. How many ways are there to transport all three across?
Editorial convention: part 4 counts shortest routes; distinguish the source’s outward-trip numbering from one-way crossings. Answer all four parts.