There is an eight-litre jug full of water and two empty jugs; one
of them can hold five litres of water and the other three litres.
If the water is to be shared equally between two people, how can this
be done?

Fill the five-litre jug from the eight-litre jug. From the five-litre
jug, fill up the three-litre jug. Pour the water from the three-litre
into the eight-litre jug. Pour the remaining amount of water in the
five-litre jug (two litres) into the three-litre jug. Fill the
five-litre jug from the eight-litre jug (which previously held six
litres and now holds one litre). Fill the three-litre jug using one
litre from the five-litre jug. Then add the contents of the three-litre
jug to the eight-litre jug. Both the five-litre jug and the eight-litre
jug each now contain four litres.

For further thought: Given *any* sizes of jugs, under what
conditions can the water be equally divided? You may want
to have a look at my congruence page.