The key to answering the stranger questions is not to get flustered by them. Most of the time the answer that you give won't really matter, as many of these questions don't have a correct answers.

Some of the questions are there to allow the interviewer to see how you think, and your analytical process. No-one knows how many trees there are in the United Kingdom but you could make an estimate based on common knowledge or estimates of trees per mile square.

How many hats are there in the United Kingdom? The art of answering this question is to use both your general knowledge and show confidence that you're willing to have a shot at it. There is a right answer to this but no-one is going to know. Suggested methods of answering this question is to start with a little general knowledge and build from there. i.e. there are about 60 million people and lets say they have on average two hats...and then you might want to go on to talk about hats still in the shops or in hat factories. Keep the numbers simple so you don't mess the maths up.