This Kangaroo is jumping!
There is nothing in education quite like the Kangaroo. A multiple-choice maths challenge sat by more than seven million children in around 120 countries, from Afghanistan to Zimbabwe, it is arguably the world’s most widely-taken primary and secondary school test.
Today’s puzzle is taken from the 2024 Kangaroo. But before we get there, some background.
The first Kangaroo was held in France in 1991. It was inspired by an Australian maths challenge that has been running since the 1970s, hence the name. Other European countries soon came on board and, since around 2000, so did the rest of the world. The country with highest participation is Brazil (1.8 million pupils), followed by Germany (900,000), France and Poland (both 300,000).
The purpose of the Kangaroo is to promote the enjoyment of mathematics. The questions vary in style every year, and are designed to test problem-solving skills and clear thinking.
“We want to share our passion for the beauty of mathematics with everyone,” said Meike Akveld, a Swiss mathematician who is president of the Association Kangourou Sans Frontières (AKSF). “I like to think of the Kangaroo as the sports day of mathematics. It is for everyone, at all levels.”
The Kangaroo is divided into six age levels: lower and upper primary; lower, middle and upper secondary; and sixth form. The questions are set by the AKSF and distributed by national associations, who decide how many questions to use for each level and how long pupils are allowed. Usually, the papers are sat on the third Thursday in March, and last around an hour.
Today’s problem was the final question in the 2024 sixth form paper, making it the hardest question that year. Not many children would be expected to get it right. But it is certainly within the capabilities of a top GCSE student.
The four powers
A four digit number abcd satisfies the equation abcd = aa + bb + cc + dd.
What is a?
[Note: abcd means that the first digit is a, the second is b, the third is c and the fourth is d. It does not mean a x b x c x d. The numbers a, b, c and d do not have to be different.]
As an extra, what are b, c and d?
I’ll be back at 5pm UK with the solution.
PLEASE NO SPOILERS. Please discuss marsupials, mass-participation mathematics and multiple choice.
The Kangaroo currently has a relatively small reach in the UK, with only about 21,000 Brits taking part this year, about the same numbers as in Mexico and Serbia. One explanation for this low number is that we already have a well-established system of national mathematical challenges, run by the UK Mathematics Trust (UKMT). The UKMT now incorpoates three levels of Kangaroo within its ecosystem, however, and participation is likely to grow.
The movement is also being helped by the Kangaroo Maths Trust, a UK-based charity established earlier this year with the financial support of algorithmic trading fund XTX Markets.
Indeed, the Kangaroos are bounding out in all directions. This year the AKSF launched the first Kangaroo Open, for adults, and next year will run a Kangaroo for children under 6. You’re never too young for multi-choice maths!
For more information about entering the Kangaroo in the UK, contact the UKMT. For all other countries, find your national Kangaroo association here.
You can read previous Kangaroos in the World Olympiads Bank, an archive of almost 100,000 problems from international competitions in maths, physics, chemistry, biology informatics and astronomy. In the Kangaroo section, the levels are Pre-Ecolier (lower primary), Ecolier (upper primary), Benjamin (lower secondary), Cadet (middle secondary), Junior (upper secondary), Student (sixth form).
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
