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# Vector Racer

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### Consecutive Numbers

### Pair Sums

### Negative Dice

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Age 11 to 16

Challenge Level

*Printable sheets: Instructions, race track 1, race track 2 (avoid the pits)*

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?