Playing pencil and paper games can help you build your mathematical skills – logic, planning, and spatial perception. For the holiday weekend, Occupy Math gives you three such games.

**Play these games with family and friends while waiting for dinner or in case the half-time show does not meet the standard.**

The game of **pipes** starts with interleaved grids of open and filled circles. The players take turns connecting dots that are next to one another, horizontally or vertically, with the restriction that you cannot cross the other player’s line. The goal is to make make a path all the way across the board as this animation shows:

## Pipes

Pipes is a game that helps you learn to plan ahead – not as much as chess, but it is good practice.

The game of **capture** starts with a grid of dots. Players take turns making vertical or horizontal lines between adjacent dots. If a player completes a square they *capture* that square – usually they put their initials in it. When you capture a square, you get to move again. This can create cascades of captures making the game exciting. The winner is the player with the most captures – the green player wins the game below.

## Capture

Capture is similar to pipes in its ability to help you learn to plan, but the ability to move again means that the end comes much faster.

**Sprouts** has the simplest starting configuration: you put some dots on a piece of paper. The rules are as follows.

- The players take turns connecting two dots.
- You cannot cross another player’s line.
- After you draw a line, you put a new dot in the middle.
- You may not begin or end at a dot that already has three lines.
- The winner is the last player to move.

The way sprouts plays out depends a great deal on the way the lines players draw change the connectivity of the remaining space. The animation below shows several of the ways you can move.

## Sprouts

Notice that the animation X’s out dots that cannot be used again. Sprouts helps people understand about *connectivity*. The game of sprouts that starts with three dots is not too hard to understand. As you add dots the game gets much more complex.

All three of these games help players develop mathematical skills – but not numerical ones. There are three great branches of mathematics. **Analysis** is what calculus turns into if you keep going. **Abstract algebra** is the generalization of the kind of math that arises from studying the properties of the integers and from studying symmetry. **Topology** is the field that arises from continuing the study of geometry.

**The three games in today’s Occupy Math are in the domain of topology.**

Know any other good pencil-and-paper games? Got apps that play these? Tweet or comment to let other readers know.

I hope to see you here again

Daniel Ashlock

University of Guelph

Department of Mathematics and Statistics

Quoridor (I believe that’s the right spelling, with just one “r” in the middle) reminds me of pipes.

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