Recently Chinese 11-year-olds faced the following question in a maths exam. ‘If a ship has 26 sheep and ten goats on board, how old is the ship’s captain?’ Chinese social media lit up with parents furious at their little emperors being asked a question they could not answer.

The BBC did find one Weibo user who had devised a plausible solution. ‘The total weight of 26 sheep and ten goats is 7,700kg. In China, if you’re controlling a ship with over 5,000kg of cargo you need to have possessed a boat licence for five years. The minimum age for getting the licence is 23, ergo the captain is at least 28.’ But if this were the desired answer, it would seem to require a freakish childhood obsession with nautical regulations, and, as a Welshman, I can’t help pointing out that the solution has been obtained only by assuming a cargo of remarkably chubby livestock.

Thankfully some internet detectives went to work on the question, among them Presh Talwalkar of the MindYourDecisions YouTube channel. It turns out this puzzle has its origins in France, in a letter from Gustave Flaubert to his sister in 1841. Then, in 1979, a shorter version, identical to the later Chinese question, was posed verbatim to French schoolchildren as a psychological experiment. The aim was to find out if the assumed certainty implicit in maths tests would lead people to give definitive answers at the expense of critical thinking. It did. Around three quarters of pupils answered ‘36’ (i.e. 26 plus ten) or else contrived some other number. Fewer than a quarter wrote ‘not enough information’. Similar results emerged in Germany and Switzerland.

‘Trick’ questions of this kind are commonly used in educational studies. For example water is shown dripping into a cylindrical vessel. ‘If the water level rises 3cm in ten minutes, what will the water level be after 30 minutes?’ 9cm? Hurrah! But an alternative version of the question depicted a container which tapered towards the neck. Only 5 per cent of children compensated for this.

Now consider the question: ‘My next-door neighbour has two children, one of whom is a girl. What are the odds the other is a boy?’ Leaving gender politics aside, the answer is 66 per cent. Rephrase it as ‘…the elder is a girl but I don’t know what sex the younger one is’ and the odds change to 50-50. Even highly numerate adults get floored by this.

So am I in favour of mandating maths teaching after GCSEs? Yes, but only if the time is spent repairing some of the damage done earlier. Combined with critical and creative thinking, and with a heavier emphasis on statistics, it could be both enriching and valuable. Not least because some large part of our political divisions – including both prejudice and ill-conceived attempts to assess and correct for prejudice – arises from statistical cluelessness among the otherwise educated. If the level of literacy in news media were equivalent to the level of numeracy, not only would articles be packed with grammatical errors, they’d be written in crayon with some of the letters upside down. Tim Harford’s More or Less on BBC Radio 4 should be a model for correcting this.

Besides, there has long existed a huge bias against the sciences in the choice pupils make when picking A-levels. It is tacitly understood that people who want to focus on Stem subjects must do at least three science A-levels, whereas humanities students can mix and match at will. This asymmetry has discouraged many undecided or mentally ambidextrous pupils from studying any science subject at all. It’s a Chinese restaurant style of architecture, where scientists must choose set menu A or B while artier types can go à la carte. The fact that almost no one has noticed this bias is itself evidence of our failure to teach critical thinking.