Conjecture:

Everybody in the UK has ginger hair.



Proof:

This will be a proof by induction. Let P(n) be the statement: "n people in the world have ginger hair".

Now we show P(n). Clearly we can find one person in the world who is ginger.

Now we assume that if P(n) is true, P(n+1) is true. Get any n+1 people into the UK, get everybody else out. Now, remove one of the people. Now, since P(n) is true (by our assumption), we know that all the n people in the UK are ginger. Now bring the excluded person back in and send a different person out. Again, P(n) is true so all these people are ginger-haired. Bring back the excluded person and we have n+1 people in the UK, all of whom must be ginger.

Therefore, P(n) is true for n arbitrarily large. Specifically, we can make it as large as the number of people in the UK.

So, by induction, all people in the UK are ginger.