# Pouring the Punch Drink

## Problem

a) There are four jugs.

The largest holds exactly $9$ litres of drink, and is filled to the top.

The $7$ litre, $4$ litre and $2$ litre jugs are empty.

Find a way to pour the drink from one jug to another until you are left with exactly $3$ litres in three of the jugs.

b) You have three jugs one of which is full and holds $8$ litres.

The capacity of other jugs is not known. But, it is known that when using them every whole number quantity from $1$ litre to $8$ litres can be accurately measured out.

What could be the capacities of the $2$ other jugs?

How would you measure all the whole number quantities from $1$ to $8$ litres?

## Student Solutions

This one took a lot of patience - well done!

This well explained solution comes from Gemma who goes to Foxford School and Community College, Coventry.

Remember: the jugs hold $9$, $7$, $4$ and $2$ litres, and you can't guess any amounts.

`9 0 0 0`

From the $9$ litre bottle take $4$ litres to $4$ litre
bottle.`5 0 4 0`

$4$ litres from $4$ litre bottle to $7$ litre bottle.`5 4 0 0`

Take $4$ litres from the $9$ litre bottle to the $4$ litre
bottle.`1 4 4 0`

$3$ litres from the $4$ litre bottle to $7$ litre bottle.`1 7 1 0`

$2$ litres from $7$ litre bottle to $2$ litre bottle.`1 5 1 2`

$2$ litres from the $2$ litre bottle to $9$ litre bottle.`3 5 1 0`

$2$ litres from $7$ litre bottle to $2$ litre bottle.`3 3 1 2`

$2$ litres from $2$ litre bottle into $4$ litre bottle.`3 3 3 0`

Syed also from Foxford School and Community College, Coventry has found a different solution, and presented it in a table.

Amount of drink in the jug (litres) | The Pour | |||

$9$ - litre jug | $7$ - litre jug | $4$ - litre jug | $2$ - litre jug | |

Full | Empty | Empty | Empty | Start |

$2$ litres | Full | Empty | Empty | $9$ - litre jug to $7$ - litre jug |

Empty | Full | $2$ litres | Empty | $9$ - litre jug to $4$ - litre jug |

Empty | $5$ litres | $2$ litres | Full | $7$ - litre jug to $2$ - litre jug |

Empty | $3$ litres | Full | Full | $7$ - litre jug to $4$ - litre jug |

$4$ litres | $3$ litres | Empty | Full | $4$ - litre jug to $9$ - litre jug |

$6$ litres | $3$ litres | Empty | Empty | $2$ - litre jug to $9$ - litre jug |

$6$ litres | $1$ litre | Empty | Full | $7$ - litre jug to $2$ - litre jug |

$6$ litres | Empty | $1$ litre | Full | $7$ - litre jug to $4$ - litre jug |

$6$ litres | $2$ litres | $1$ litre | Empty | $2$ - litre jug to $7$ - litre jug |

$1$ litre | Full | $1$ litre | Empty | $9$ - litre jug to $7$ - litre jug |

$1$ litre | $5$ litres | $1$ litre | Full | $7$ - litre jug to $2$ - litre jug |

$3$ litres | $5$ litres | $1$ litre | Empty | $2$ - litre jug to $9$ - litre jug |

$3$ litres | $3$ litres | $1$ litre | Full | $7$ - litre jug to $2$ - litre jug |

$3$ litres | $3$ litres | $3$ litres | Empty | $2$ - litre jug to $4$ - litre jug |

Here's a third solution from Thomas at Tattingstone Primary, UK.

9 0 0 0 2 7 0 0 2 5 0 2 4 5 0 0 4 3 0 2 6 3 0 0 6 1 0 2 8 1 0 0 8 0 1 0 1 7 1 0 1 5 1 2 3 5 1 0 3 3 1 2 3 3 3 0