Hans Woyda is a club primarily for enthusiastic and talented young mathematicians.
In principle, we train for the London Schools Hans Woyda Competition; however, we always stray off the chosen path wherever possible. This could not be better highlighted than by the solutions seen below, produced by Year 6 pupil Farhan. Miraculously, he also solved the other four questions on the two hour paper, suggesting that maybe one day he could replicate the achievements of our Head Boy, Siddiq Islam, and win a place at Oxford to read Mathematics.
Mr Leadbetter (Teacher of Mathematics)
How many numbers less than 2013 are both:
- the sum of two consecutive positive integers; and
- the sum of five consecutive positive integers?
Pippa thinks of a number. She adds 1 to it to get a second number. She then adds 2 to the second number to get a third number, adds 3 to the third to get a fourth, and finally adds 4 to the fourth to get a fifth number.
Pippa’s brother Ben also thinks of a number but he subtracts 1 to get a second. He then subtracts 2 from the second to get a third, and so on until he too has five numbers.
They discover that the sum of Pippa’s five numbers is the same as the sum of Ben’s five numbers. What is the difference between the two numbers of which they first thought?