23/10/2017

# Are you smarter than a Brazilian 15-year-old?

Teenage Brazilians using their heads. Photograph: Laurence Griffiths/Getty Images

Guzzlers, tudo bem?

Here’s a question from Brazil’s State School Maths Olympiad, one of the largest and most remarkable maths competitions in the world.

Founded 12 years ago by the Institute for Pure and Applied Mathematics in Rio de Janeiro, the Olympiad aims to improve maths education in the country’s cash-starved state school system. According to the OECD, 67.1 per cent of Brazilian 15-year-olds are low-performers at maths, compared to the OECD average of 23 per cent.

In June, more than 18 million kids in 53,000 schools from the favelas of Rio to the villages of the Amazon rainforest take a 20-question multiple choice test. There are three levels: for 11 and 12 year olds, for 13 and 14 year olds and for 15 to 18 year olds. The top 5 per cent of each school sit a second exam in September, which consists of 6 harder questions.

Today’s question is from a recent paper for 15 to 18 year olds.

Homero is clutching three identical pieces of string in his fist, as illustrated below left. He asks Sofia to tie two ends of the string, chosen at random, at either side of his fist, as illustrated below centre, so that there is one free end at either side.

When Sofia ties two ends either side there are two possibilities: the string is now all joined together in one piece, or one piece is disconnected from the other two.

1) What is the probability that all the pieces are joined in one long piece?

Now Homero is clutching five identical pieces of string in his fist, in the same way as above. On each side of his fist there are five ends. On each side Sofia ties together free pieces of string, leaving a single end free either side. (So she makes four knots in total.)

2) What is the probability that one piece of string is not connected to any other?

3) What is the probability that all the pieces are joined in one long piece?

Children who win gold, silver or bronze medals in the olympiad are invited to take part in educational science programmes for gifted children. Already academic research shows that the olympiad is improving overall maths performance, and medal-winners have gone on to study at Brazil’s top universities, as well as at places like Harvard and Princeton. Gooooooal!

I’ll be back with the answers to today’s puzzle at 5pm. Meanwhile, NO SPOILERS PLEASE!

Thanks to Marco Moriconi for letting me know about the State School Maths Olympiad.