Are you clever enough for Oxbridge?

Do you think you're clever?

(Law, Cambridge)

Answer, modestly, "no" and the interviewer might take you at your word and deny you a place at Oxbridge where only clever people are admitted (so rumour has it). Answer "yes" and you risk suggesting that you're a fool. The interviewer is bound to be, by virtue of his position (on the other side of the interview), cleverer than you – and by suggesting you might be on his level, you are heading for a fall! If you hedge your bets with a non-committal answer, you look like someone who is too vacillating and lacking incisiveness to be an Oxbridge star ...

Ever since the days of Ancient Greece, being clever has had rather negative overtones. Cleverness, according to Aristotle, was the mere capacity for figuring out how to achieve something, without the attending touchstone of virtue. Plato was equally scathing, saying: "Ignorance of all things is an evil neither terrible nor excessive, nor yet the greatest of all; but great cleverness and much learning, if they be accompanied by a bad training, are a much greater misfortune." Ever since, cleverness has had the image of being a rather dubious quality, linked with underhand cunning on one side and braggadocio on the other. Milton's Satan was dubbed "clever".

So admitting that you are clever can be tantamount to announcing that you are either devious or a braggart – or even a fool because no one who was wise would believe that they were clever, and no one really clever would openly admit to being clever. Even the brilliant Oscar Wilde had to announce his cleverness with self-deprecating wit, saying, "I am so clever that sometimes I don't understand a single word of what I'm saying", which is probably the perfect answer to the question.

Should someone sell their kidney?

(Medicine, Cambridge)

Ever since organ transplants first became common in the 1960s, there has been a problem sourcing suitable donor organs. Most kidneys for transplant come from dead donors, but since people can usually survive with just one of their kidneys, they can also come from living donors – about one in 10 in the UK do and one in four in the USA. Kidneys from living donors are generally in better condition, and there is a better chance of finding a good match, especially among relatives.

The problem is that not everyone has a generous relative sitting by, which is why desperate kidney sufferers in the world's richer countries may look for a donor in the developing world. Donating a kidney is not an everyday, harmless procedure. Undergoing the operation can be traumatic, and very occasionally fatal.

Interestingly, the question comes at the issue from the donor's point of view and asks should the donor sell a kidney. As a (comparatively!) rich Westerner, of course I can't say the donor should sell, and yet nor can I disapprove of the donor who chooses to sell. I would never want anyone put in the position where they are tempted to sell a kidney, but I can understand how someone would accept the suffering and risk to give themselves or their family a better life. To the question "should someone?", the answer must clearly be "no" – because that is a question only the donor can decide.

What percentage of the world's water is contained in a cow?

(Veterinary Medicine, Cambridge)

Whatever the answer to this question is, it's going to be very small. The number of cows on the planet has increased dramatically in the last few decades as more people turn to meat and dairy products. There are now about 1.3 billion cows on earth. So the percentage of water in a single cow of all the water in just cows alone is much less than a billionth of a percent, or 0.000000001 per cent.

The human body is largely water – about 70 per cent by weight – and the chances are that other mammals have much the same water content. You could guess that the average cow weighs about 500 kg, which would mean it contains about 350 kg of water – about 350 litres.

It's harder to estimate of the volume of water in the world. Ignore all the freshwater, ice and atmospheric moisture (which is less than 3 per cent of the total) and concentrate on the oceans. Assuming that about three-quarters of the earth is covered in water, you can work out the area of the oceans from the formula for the surface area of a sphere, which is four times pi times the radius squared, or 4p × r2. The radius is 6,400 km. Squared that's 41m. Four times pi is about 12.5. So the surface area of the earth is very roughly 500m sq km. Three-quarters of that is about 360m sq km. The oceans are probably about 4,000m deep on average. So the volume of the water in the world is 360 times 4,000 cu km – that is, 1,440,000 cu km, or 1,440 million billion litres. So to work out the percentage of water in the cow, we divide the volume of the world's water by the volume of water in the cow and multiply by 100. The answer is about 0.00025 billionths of a per cent, or 0.0000000000025 per cent.

If you're not in California, how do you know if it exists?

(Geography, Oxford)

On a practical, everyday basis, it makes no sense to challenge the existence of California, even if you're not there to experience it directly. You can cross-check its existence from different sources – some eminently trustworthy, such as important reference books and atlases, some perhaps less trustworthy, such as, say, your next door neighbour. There are not just written accounts, but photographs as well of places within California and photographs of the entire state from space, not to mention all those Hollywood movies.

Every source you try will usually confirm that California exists. It's highly unlikely that any source at all will say California does not exist. What's more, you could ring up someone in California and ask them to confirm that it's still there. In fact, from your knowledge of the rest of the world, you could probably be pretty confident that there was at least something in that space between the Pacific and the American midwest.

It might all be an incredibly elaborate subterfuge – a worldwide conspiracy designed to fool you into believing in California, for instance, or an elaborate holographic mirage that even "visitors" and "residents" in California are completely convinced by. Or you might just be delusional. But with such multiple, varied sources of information, the odds are so completely stacked in the favour of California's existence that for all practical purposes you can assume it exists – until you have evidence to the contrary.

What would happen if the classics department burned down?

(Classics, Cambridge)

I'd say the interview just might have to be rescheduled... If the department burns down, the fire must have been so severe that the fire brigade were unable to stop it. That would be a shock in a modern building, incorporating a fire alarm, sprinkler systems and fire doors. So if the Classics department did burn down, questions would have to be asked. Why did the fire brigade fail to deal with the blaze? Were they slack in any way, either in arriving fast enough, or in dealing with the fire? Or was the fire started in several places simultaneously – or maybe involving accelerants, which would indicate arson?

The biggest concern is the contents, and this is perhaps what the question is after. The department's great prize is its classical plasters. In the Victorian era, plaster casts of classical pieces were very popular. But in the 1950s they fell out of fashion, and many collections were broken up. The Cambridge faculty is a rare and valuable survivor. One hopes that the fire progressed slowly enough for the most precious casts to have been rescued, but there are more than 400 so the chances are that some were lost.

Research work, computers and data, and the library might also have been destroyed if they could not be evacuated in time. That would mean a massive interruption to the functioning of the department, and it's possible that courses might be suspended for a year or so while resources were rebuilt.

What makes you think I'm having thoughts?

(Mathematics and Philosophy, Oxford)

The simplest answer is: my mind. The one thing that I can be certain of is that I am thinking, and it's reasonable to describe the location of my thoughts as my mind. Whether my mind is actually right is a different matter.

As many philosophers have recognised through the ages, there is no way of logically proving that my own experiences are actually real. It's equally impossible to prove that you too have a separate mind with its own independent thoughts. However, all my life experience confirms that things are as I believe them. I am aware of my body feeding back sensory information and responding to my commands. I am aware that things happen in a largely predictable way. Even when they are unpredictable, they seem to confirm my view that there is a real world beyond me, filled with real people who are having their own thoughts, just like me.

For everyday practical life it makes sense to go with the commonsense view. I live as if the evidence of my experience and my senses is true, and that you are another human being, with a mind just like mine, and that you are having thoughts just like me. So that's what "makes" me think you are having thoughts.

Do You Think You're Clever? is published by Icon Books UK (£12.99). To order a copy for the special price of £11.69 (free P&P) call Independent Books Direct on 08430 600 030, or visit Independentbooks direct.co.uk