# Maths Challenge + Alton College = Success!

Lucy Bayliss, previously at Amery Hill School and Sara Garanito, previously at Calthorpe Park School took part in this year’s Mathematical Olympiad for Girls. Over 1700 girls nationwide participated, with the top 25% receiving a Certificate of Distinction. The Mathematical Olympiad for Girls is an event run by the UK Mathematics Trust, introduced in 2011 to help schools and college nurture the talent of enthusiastic young female mathematicians. Sara received a Certificate of Participation and Lucy a Certificate of Distinction getting 10/10 for one of the questions (*below).

100 Maths students recently competed in the Senior Maths Challenge with 9 achieving a gold award, 31 a silver award and 29 a bronze. Roughly 100,000 students took the Challenge this year with an increase in participants from Alton College. The Senior Maths Challenge consists of 25 very difficult non-calculator multiple-choice maths questions to be completed in 90 minutes. Students start with 25 marks, get 4 marks for each correct answer and lose 1 mark for each incorrect answer, to discourage guessing. See www.ukmt.org.uk/individual-competitions/senior-challenge/ for more information about the Challenge, along with the paper and solutions.

The College’s top scorer was Peter Morris, previously at Eggar’s School; he scored 109 out of 125 which means he goes through to the British Maths Olympiad Round 1 (BMO1). Only the top 1000 students in the country qualify for the BMO1. A further nine students have got through to the Senior Kangaroo (SK) round, this involves the next 6000 best students, who don’t qualify for the BMO1.

They are:

Harry Buchanan, previously at Perins School

Lucy Bayliss, previously at Amery Hill School

James Dedman, previously home educated

Marco Li, previously educated overseas

Cameron Neasom, previously at Bohunt School

Rebekah Aspinwall, previously at Amery Hill School

Sam Bishop, previously at St Edmunds School

James Macmillan Clyne, previously at Bohunt School

Joe Parry, previously at The Petersfield School

Three examples of this year’s challenge are (an easy, medium and hard question):

Q2: Last year, an earthworm from Wigan named Dave wriggled into the record books as the largest found in the UK.

Dave was 40 cm long and had a mass of 26 g. What was Dave's mass per unit length?

A: 0.6 g/cm B: 0.65 g/cm C: 0.75 g/cm D: 1.6 g/cm E: 1.75 g/cm

Q11: The teenagers Sam and Jo notice the following facts about their ages:

The difference between the squares of their ages is four times the sum of their ages.

The sum of their ages is eight times the difference between their ages.

What is the age of the older of the two?

A: 15 B: 16 C: 17 D: 18 E: 19

Q24: There is a set of straight lines in a plane such that each line intersects exactly ten others.

Which of the following could not be the number of lines in that set?

A: 11 B: 12 C: 15 D: 16 E: 20

^{Answers are B, D and D.}

The question Lucy got totally correct:

*Let n be an odd integer greater than 3 and let M = n ^{2} + 2n − 7.*

*Prove that, for all such n, at least four different positive integers (excluding 1 and M) divide M exactly.*

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