| By clue 1, the Pilgrim family who owned Kate ended up trading for the sheep.
The Whites got a horse out of the swapping (clue 2), so they are the 2nd
family to trade. The family who had the horse ended up with Bessie (4);
they can't be the Whites or the family who got the sheep (7) and must be
the 3rd family. Then, since Bessie couldn't have been the horse and since
no two families simply traded animals (10) so that Bessie wasn't swapped for
the horse, the family that owned Bessie before trading is the 4th family.
By clue 7, Bessie wasn't the sheep; therefore, either the sheep was owned by
the 5th family or the sheep was owned by the Whites. If the sheep had been
owned by the 5th family, by clue 8, the pig the Mullins traded would have
been Bessie. Since Kate was never owned by the Mullins (8), Kate would have
been the animal the family who traded the sheep got in return. However,
there would then have been a simple trade of Kate for the sheep between two
families, contradicting clue 10. So, the sheep can't have belonged to the 5th
family and was owned by the Whites. By clue 8, the Mullins traded away the pig
and never owned Kate, so either the Mullins are the 5th family or Bessie
was the pig. Trying the first case, Bessie would have brought Kate in
return. But Kate or Bessie then would have been the pig, a conflict. Therefore, the
Mullins traded Bessie the pig. They did not get Kate in return (8), so
Kate went to the 5th family. Since the Allertons got Prissy in the swap
(5), Prissy must be the sheep they traded Kate for. By clue 3, the
Hopkinses didn't get the cow or goat; they got Bessie the pig. By
elimination, Kate went to the Brewsters. The Brewsters didn't trade away
the goat (9) and traded away the cow--for Kate the goat. The cow went to
the Mullins family. By clue 6, Molly was the cow and Annie the horse.
In sum, the Pilgrim families swapped livestock as follows:
- the Allertons traded Kate the goat for Prissy the sheep
- the Brewsters traded Molly the cow for Kate the goat
- the Hopkinses traded Annie the horse for Bessie the pig
- the Mullinses traded Bessie the pig for Molly the cow
- the Whites traded Prissy the sheep for Annie the horse
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