Pouring the punch drink

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Age

7 to 11

Challenge level

Being curious Being collaborative Being resourceful Being resilient

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

The children at Kambala School in Australia worked hard on this problem and found a different way of reaching the solution. Mia filled in this table to show what they did:

Pour	9L jug	7L jug	4L jug	2L jug
Start	9L	0	0	0
Fill up 7L from 9L	2L	7L	0	0
Fill up 4L from 7L jug	2L	3L	4L	0
	5L	0	4L	0
	5L	4L	0	0
	1L	4L	4L	0
	1L	7L	1L	0
	1L	5L	1L	2L
	1L	5L	3L	0
	1L	3L	3L	2L
	3L	3L	3L	0

Can you see what's similar and different about Mia and Gemma's solutions?

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

Thank you to everybody who shared their solutions with us!

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Pouring the punch drink

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