Are you smarter than a 15-year-old Brazilian?
Hey smarty pants, how's it going?
Here is a question from the Brazilian Public School Mathematics Olympiad , one of the largest and most notable mathematics competitions in the world.
Founded 12 years ago by the Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro, the Olympiad aims to improve mathematics education in the country's struggling public school system. According to the OECD (Organisation for Economic Co-operation and Development), 67.1% of 15-year-old Brazilians show low performance in mathematics. The OECD average is 23%.
In June, more than 18 million children in 53,000 schools, from Rio's favelas to villages in the Amazon rainforest, took a 20-question multiple-choice test. There are three levels of competitors: students aged 11 and 12, 13 and 14, and 15 to 18. The top 5% from each school take a second exam in September, consisting of six more difficult questions.
Today's question is part of a recent article for the 15-18 age group.
Homer is holding three identical pieces of string, as illustrated below on the left. He asks Sofia to tie two ends of the strings, chosen randomly, to either side of her wrist, as shown in the center illustration, so that one end is free on one side.
Quando Sofia amarra duas extremidades de qualquer dos lados, há duas possibilidades: o fio agora está unido em uma única peça ou uma peça é desconectada das outras duas.1) What is the probability that all the pieces are joined in one long piece?
1) What is the probability that all the pieces will come together to form one long piece?
Now, Homer is holding five identical pieces of string in his hands, in the same way as above. On each side of his hands, there are five ends. On each side, Sofia ties the loose ends of string, leaving a single free end. She ties four knots in total.
2) What is the probability that a piece of wire is not connected to any other?
3) What is the probability that all the pieces will come together to form one long piece?
Students who win gold, silver, or bronze medals in the Olympiad are invited to participate in science programs for gifted children. Academic research shows that the Olympiad is improving overall performance in mathematics . Medalists have gone on to study at top universities in Brazil, as well as universities like Harvard and Princeton. Gooooool!
Thanks to Marco Moriconi for informing me about the Brazilian Mathematics Olympiad for Public Schools.
Reproduction: https://www.theguardian.com/science/2017/oct/23/can-you-solve-it-are-you-smarter-than-a-brazilian-15-year-old