Four Sheep

I like including warm-up puzzles with every homework.

Puzzle. Farmer Giles has four sheep. One day, he notices that they are all standing the same distance away from each other. How can this be so?

The expected answer: The configuration is impossible in 2D. So, one of the sheep is on a hill or in a pit.

Some students thought big: The sheep could be placed at different locations around the Earth, forming a really big tetrahedron. In this case, we need to explain what it means for the farmer to “notice”, but this minor issue could be resolved in many ways.

Some of the students questioned the meaning of the word distance. They argued that if sheep are all touching each other, they are the same distance 0 from each other. One way this could happen is if the tails of the four sheep were entangled.



  1. lvps1000vm:

    A sheep is at 2nd avenue with 1st street. The others are at 1st with 2d, 3rd with 2nd and 2nd with 3rd. They are all at the same Manhattan distance.

  2. Leo B.:

    Seconding @lvps1000vm, “Gilles is a French and *Dutch* personal name”, so, ignoring spelling minutia, it could be said that the intended answer is “Manhattan distance”.

  3. Zarunias:

    Farmer Giles also has a dog. Its name is “each other”.

  4. Guido:

    I know nothing about Farmer Gilles, but Farmer Giles has indeed a Dog. He also has a Dragon: Dog and Dragon are the “others” (neither Farmer Giles nor sheep). The sheep, fearful of both, group themselves at the midpoint between them…

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