Here at PopMech, we love mind-bending math and logic puzzles, which is why we regularly recruit the sharpest minds in the world to concoct riddles that will test your critical thinking, mathematics, and logic skills. The following riddle is one particularly punishing problem—so go grab a pencil and a piece of scratch paper and prepare to rip your hair out (in the best way). No cheating!

➡ The Problem

A farmer has raised his fox to protect a flock of chickens. While the fox is afraid of the chickens’ large talons, no amount of training can ever completely get rid of a fox’s carnivorous nature.

One day, the farmer heads out on a journey, taking along the friendly fox, two chickens, and a huge sack of chicken feed. When the group gets to a river, the farmer finds only a small boat with three seats—including one that the farmer must sit in—to cross the stream.

The farmer pauses and considers all options:

  • The farmer can only row two animals across the stream at once.
  • The sack of feed is huge and takes up both seats in the boat.
  • The cowardly fox will run away forever if it is left alone with two chickens.
  • The fox is hungry and will eat a chicken if only the two of them are ever left alone.
  • The chickens are also hungry, and either one will eat the feed if they are ever left alone.

The farmer looks at the boat and lets out a long sigh. How can he safely get the whole crew—including the feed—across the river?

➡ The Solution

The farmer has a few problems to avoid during this little trip.

#1: The fox can never be left alone with the chickens, either one-on-one or with the pair. #2: While the farmer has to keep a close eye on the fox, it’s also important to make sure neither chicken is left alone with the sack of feed.

With those instant failure conditions in mind, we need to build a table to track the farmer’s movements. First things first, we’re moving these chickens.

logic puzzle table
Richard Malena

While the problem is solvable, it turns out that the farmer did train the fox in vain. The crossing fails as long as the fox and a chicken are ever together in any quantity, trained or not.

This is a variation of the classic river-crossing riddle. Have a favorite? Send it my way. The puzzle community really needs to work together to help these farmers out.

➡ Pro Perk: Chat With the Puzzle Coach!

Curious to know more about this particular problem and solution? Stumped by another riddle and want the secret to solving it? I’d love to hear from you. Email me with your questions and we can nerd out over all kinds of puzzles, math problems, and brain teasers together!