Who ate all the tarts? QE boys know the answer

Who ate all the tarts? QE boys know the answer

The number of QE pupils receiving top awards in the UKMT Intermediate Maths Challenge has increased again this year, with one boy achieving a perfect score.

The IMC competition, run by the UK Mathematics Trust, is for pupils in Years 9 to 11; 317 boys from QE took part – 174 were awarded gold certificates (up from 172 last year), while 103 were awarded silver (compared to 91 last year), with a further 31 receiving bronze.

Ansh Jassra from Year 10 was awarded Best in School, scoring a maximum-possible 135 points.

With only 500 places available nationally across all schools for the highest scorers for the Intermediate Olympiad, Ansh and 22 other QE boys qualified. A further 174 QE pupils secured entry into the Intermediate Kangaroo, the competition’s other follow-on round.

Ansh said: “With its many challenging yet intriguing maths problems, sitting the IMC was fun, testing and overall a great experience. I am looking forward to the Olympiad!” said Ansh.

Assistant Head of Mathematics Wendy Fung said: “We are delighted with how well the boys have done and extremely pleased with the continued increase in the proportion of boys reaching the follow-on rounds. As the recently introduced 9-1 GCSE has a strong focus on problem-solving, success in the IMC will stand the boys in good stead for their examinations.”

Maxwell Johnson, who was named Best in Year 9 with a score of 130, said: “I hope that I will be able to improve on my score in the [Junior] Olympiad from last year. It will be challenging, but I’m sure I will enjoy it.”

Shimaq Sakeel Mohamed, who also scored 130 and was named Best in Year 11, said: “I am proud to be part of a School where I can achieve great things and the IMC is a great way to do this.”

Sample question:
The Knave of Hearts stole some tarts. He ate half of them, and half a tart more. The Knave of Diamonds ate half of what was left, and half a tart more. Then the Knave of Clubs ate half of what remained, and half a tart more. This left just one tart for the Knave of Spades.

How many tarts did the Knave of Hearts steal? A. 63  B. 31  C. 19  D. 17  E. 15

Solution:
Suppose that at a particular stage there are m tarts available for a Knave to eat and that there are n left after he has finished eating. Then n = m − ( ½ m+ ½ ) = ½ m – ½ . Therefore, m = 2n +1. As the Knave of Spades received one tart, then the number of tarts which the Knave of Clubs was given was 2×1+1 = 3. Similarly, the number of tarts which the Knave of Diamonds was given was 2×3+1 = 7. Finally, the number of tarts which the Knave of Hearts stole was 2×7+1. So the correct answer is: E. 15.