Challenge Level

To play this game, you will need to print off a copy of the race track, and you will need someone to play with.

**Rules:**

Each player moves in turn, and uses vector notation to describe their moves around the race track.

Each player starts off from rest.

Each horizontal and vertical component **cannot differ by more than two** from the previous move.

For example, after a move of $\pmatrix{0\cr 2}$ the following moves are possible:

$\pmatrix{-2\cr 0}$ | $\pmatrix{-1\cr 0}$ | $\pmatrix{0\cr 0}$ | $\pmatrix{1\cr 0}$ | $\pmatrix{2\cr 0}$ |

$\pmatrix{-2\cr 1}$ | $\pmatrix{-1\cr 1}$ | $\pmatrix{0\cr 1}$ | $\pmatrix{1\cr 1}$ | $\pmatrix{2\cr 1}$ |

$\pmatrix{-2\cr 2}$ | $\pmatrix{-1\cr 2}$ | $\pmatrix{0\cr 2}$ | $\pmatrix{1\cr 2}$ | $\pmatrix{2\cr 2}$ |

$\pmatrix{-2\cr 3}$ | $\pmatrix{-1\cr 3}$ | $\pmatrix{0\cr 3}$ | $\pmatrix{1\cr 3}$ | $\pmatrix{2\cr 3}$ |

$\pmatrix{-2\cr 4}$ | $\pmatrix{-1\cr 4}$ | $\pmatrix{0\cr 4}$ | $\pmatrix{1\cr 4}$ | $\pmatrix{2\cr 4}$ |

Challenge a friend to a race.

Choose your starting positions and agree what the penalty will be for going off the track.

**Who can get round in the fewest moves?**

”‹Here is an alternative version you might like to try.

The challenge is to avoid the pits.

**Extension:**

Who can get round in the shortest distance?