A general paper from the 2011 Eton scholarship exam has been exhumed and is doing the rounds. The first question required candidates to read a passage from The Prince ('it is much safer to be feared than loved' etc) and then (a) summarise the argument in no more than 50 words (5 marks); (b) in their own words say what they find 'unappealing' about the argument (5 marks); and (c), for 15 marks:

The year is 2040. There have been riots in the streets of London after Britain has run out of petrol because of an oil crisis in the Middle East. Protesters have attacked public buildings. Several policemen have died. Consequently, the Government has deployed the Army to curb the protests. After two days the protests have been stopped but twenty-five protesters have been killed by the Army. You are the Prime Minister. Write the script for a speech to be broadcast to the nation in which you explain why employing the Army against violent protesters was the only option available to you and one which was both necessary and moral.

I wonder if any of the candidates described the hypothetical protesters' actions as 'criminality pure and simple'.

'The question has been quoted out of context,' according to Eton's headmaster, Tony Little.

The previous part asked them to say what was unappealing about Machiavelli’s ideas, we are looking for candidates who can see both sides of an idea and express them clearly – both directly and through more imaginative writing.

High ability candidates at this level are often asked to put themselves in other people’s shoes. In that regard this is no different from a GCSE English question which might ask: 'Imagine you are Lady Macbeth, write a diary entry to express your feelings on receiving your husband’s letter.'

In other regards, though, it is quite different. It's fairly unlikely, for example, that any of the boys who sat the exam will find themselves in adult life encouraging their spouses to murder their way to the Scottish crown. But it's far from unimaginable that one of them will be prime minister in 2040. Of Britain's 53 prime ministers from Walpole to Cameron, 19 (more than a third) went to Eton, including both Walpole and Cameron.

'We don’t favour any particular political viewpoint,' Little says. And yet for some reason all six Old Etonian prime ministers since 1900 have been Tories. Twenty Old Etonians were elected to the House of Commons in 2010; all of them sit on the government benches (19 Conservatives, one Lib Dem). And none of them, if government policy is anything to go by, seem to be much good at putting themselves in other people's shoes, except possibly each other's.

The exam paper ends with some maths questions: 'Peter is having a large conservatory built at the back of his house... How many days’ labour will Peter have to pay for?'