As Charlie comments he has "made both
countries richer". Suryasnato Dasgputa answers this:
In general to increase the average in both countries, someone
with an income between $£16,000$ and
$£20,000$ (but not exactly either) needs to move from
Emerald to Flint, for the reasons above.
2) Decreasing the average income in both
3) Increasing one whilst decreasing the
There are four ways of this happening.
1) Charlie earns over $£20,000$, and moves from Emerald
to Flint. Then Emerald's average goes down and Flint's goes
2) Charlie earns over $£20,000$and moves from Flint to
Emerald. Then Flint's average goes down and Emerald's goes
3) Charlie earns less than $£16,000$ and moves from
Emerald to Flint. Then Emerald's average goes up and Flint's goes
4) Charlie earns less than $£16,000$ and moves from
Flint to Emerald. Then Flint's average goes up and Emerald's
average goes down.
4) Moving from Emerald to Flint, reducing the
average in Emerald and doubling the average in Flint
Thomas Hu from A Y Jackson school answered
Well done Thomas, but you haven't explained
where you got these equations from. However with a little algebra,
we can see where these came from.
5) Other interesting circumstances
To change the average income of one, and not change the other by
moving either way, Charlie must have exactly the income amount of
To make one country not have a valid average income, he must be
the only citizen of a country. As average is not valid with only
one piece of information.
Suryasnato also noted;
Charlie's move would have unexpected results if when he is about
to move, a fire hits Flint and all of the below average earners are
wiped out. Then, the average income is increased to
$£20,000$. So when Charlie moves, he will be a below
average earner and make Flint poorer.
True, though we hope a fire wouldn't wipe out
half the residents of an island!
Thomas and Surysnato have spotted some
interesting changes, can you find any others?