**Last Math Monday: Wolves & Sheep**

This last Monday guest host Spencer Bowen, who leads the San Francisco math circles, led us in a classic mathematical puzzle called Wolves & Sheep. Solving this puzzle is well within the reach of all children (and even adults), and requires a willingness to keep trying things until you find a solution.

- Here’s the slidesh[ow from the event, including instructions for games you can play at home.
- And here’s a video replay of the event.

**Make up your own Variations**

I independently discovered essentially the same puzzle many years ago when I was writing puzzles for Discover Magazine. I called it “Queens at Peace”, and I framed it as a chess problem — place 10 black and 10 white queens on a chessboard so queens of opposite colors don’t attack each other. See the attached puzzle from Discover for details.

As a puzzle designer, I often invent new puzzles by taking an existing puzzle and changing one of the rules. The puzzle I started with was the classic “8 queens problem”, which is to place 8 queens on a chessboard so no two queens attack each other.

I encourage you to make up your own variations on the Wolves & Sheep puzzle. Keep at it, and it’s quite likely you’ll come up with a question that no one else has ever asked.

Start by considering what happens on larger (or smaller) boards. You can also try other types of pieces. How many black and white rooks can you place on a chessboard so rooks of opposite colors don’t attack each other? How about knights?

You can also vary a puzzle by keeping the rules the same, but changing the story. What characters could you use instead of wolves & sheep?

**Links and resources**

The wolf/sheep illusion on the first slide is from this video on YouTube, which contains a dozen pictures that can be seen in two different ways.