Take a string of six numbers. You chose the first two digits and a computer fills in the rest. The aim: to hit 100 at the end of the sequence. Only seven pairs of numbers will do the job. You have to find them all.
Confused? Not if you are one of the brightest 13-year-olds in the world.
The brightly coloured puzzles, maths teasers and tests of lateral thinking are the first of the Government's new "world-class tests", a unique attempt to create an international standard for the brightest 10 per cent of 9- and 13-year-olds.
The Independent has been given exclusive access to the new tests which are currently being taken by 8,000 primary and secondary school children at home and abroad as part of international trials.
Children in Britain are being joined by youngsters in 50 schools from as far afield as the United States, New Zealand, China, Hungary and the Netherlands in the trials.
They are witnessing the future. Bright children in all schools will be able to try their hand at the tests from September next year. And a campaign of international marketing is planned to make the tests being developed in London's Piccadilly by the Government's exams agency, Qualifications and Curriculum Authority (QCA), the global benchmark for clever children. To do this the plan would be to sell the tests abroad for use in schools.
The tests' big brother, known as the "Advanced Extension" paper, is also under development in 14 subjects. The new AE-level will be designed to stretch the very best A-level students and become an S-level for the 21st century.
Oxford and Cambridge, along with other of the nation's most prestigious universities are advising on the exams. Winchester, whose head James Sabben-Clare has been a vocal critic of A-levels, has also been involved, along with comprehensive school and sixth-form heads. The first papers are currently being written and will be tested on A-level candidates in the summer.
It all amounts to one of the largest programmes ever undertaken in Britain to cater for the nation's most able children.
David Blunkett, the Secretary of State for Education, introduced the tests as part of the Government's flagship Excellence in Cities initiative to regenerate urban schooling. Politicians have seized upon master classes and other special help for bright children as a way of tempting back middle-class parents who have abandoned inner-city state education as an option for their children.
Ministers hope the tests will identify bright children who can go on to university-based summer schools or enjoy special lessons. But these tests are not just for inner cities. All secondary schools must now develop "a distinct teaching and learning programme" for their most talented children, a move which is good news for a government bent on pursuing a message of high standards but slightly uncomfortable because it smacks of selection.
A major international consultation exercise is designed to establish the world-class nature of the tests, which may have the fortunate side effect, for the Government, of nailing the argument that British children underperform compared with their counterparts overseas.
Supporters of the new exams for high-flying 18-year-olds argue that as more and more young people gain A grades at A-level, universities see the need for an elite certificate to differentiate the exceptional from those who are merely very bright. Even critics acknowledge that there is some justification in this.
For 18-year-olds, the debate rages over the Government's choice of subjects. Latin is in, yet business studies, psychology and sociology, all highly popular A-levels, are out. The new vocational A-levels are completely written out of the script.
But many question why the world needs world-class tests for younger children, and what the certificate will mean for those who pass.
The maths and problem-solving questions that Britain's brightest will face in primary and secondary schools will be a far cry from the national curriculum tests all must sit at seven, 11 and 14.
Officials at the QCA dismiss suggestions that the tests will end up like a new 11-plus for nine- and 13-year-olds. They liken the new tests instead to the piano grades known to millions of young musicians.
The tests themselves take the form of puzzles. In one, children have to divide a five-sided shape into four triangles of equal area. In another (pictured above), they must use fractions to calculate the size of a missing portion of a triangle.
It will all be strictly optional. Teachers in primary and secondary schools will be able to put children in for the new tests at three or four points during the school year. Those who fail in one session can try the test again later in the year.
Parents, too, will be able to take the plunge, putting their children in for the tests at school or in special out-of-school centres. Sample questions will be available over the Internet. These will be designed to allow children to try the tests and act as a diagnostic tool for teachers.
The tests for nine- and 13-year-olds are being drawn up by academics at Leeds before being transferred to a multi-media computer package. They will be administered, timed and marked by computer. But children will be given old-fashioned paper to show their working and external examiners will check the results.
Those who pass will be rewarded with a qualification, and officials are considering a system of pass, merit and distinction grades to reward the most able.
Officials at the QCA insist that the stakes for children will be low and tests will not be threatening to young children. They say that they have had only positive feedback from schools and young people.
"At the moment I'm entirely clear that teachers are overwhelmingly impressed by the work that we are doing," says Martin Ripley, the manager of the tests for nine- and 13-year-olds. These tests are designed to recognise excellence and there is not a lot around that is currently designed to recognise that. Teachers will be able to take their children into summer schools and a teaching and learning environment that is related to their special needs."
Others are sceptical. "At nine and 13, I'm honestly not sure what they are for," says Professor Alison Wolff of the London University Institute of Education. "Why would a school put itself out for this?"
John Dunford, the general secretary of the Secondary Heads Association, agrees. "I can't for the life of me see the point of these tests at nine and 13 years old. We are already the most tested country in the world," he says.
"It's the job of the teacher to challenge pupils, not the assessment system. At 18 you can see the purpose of the test to distinguish between the increasing numbers of students who do pretty well at their A-levels. But for children aged just nine and 13, it's all a gimmick."Reuse content