The Mathematics Challenge
Each year, a select group of St Catherine’s students enter the Mathematics Challenge for Young Australians. This is an activity set by the Australian Mathematics Trust and is used as a training mechanism for the Mathematics Olympiad.
We are delighted to announce the following results
- In Year 6, eight girls entered. Four received a Distinction and the other four received Credits.
- In Year 7, 20 girls entered. Two received High Distinctions, five Distinctions and four Credits.
This is an intense program as the students are required to write up detailed solutions to six problems within a tight time frame in addition to their normal academic and co-curricular program. The girls in Years 8 and 9 completed part of the program, but due to other time commitments, they were unable to submit all six solutions.
I have copied the first of the six set problems for the Years 7 and 8 students for you to see the style of questioning. The emphasis is on the way the students explain their solutions rather than the actual answer. Two of our Year 7 students’ solutions are below for you to see how they approach the task. The work is from Year 7s Angela Yu and Beibei Zhang who were the two girls who achieved the impressive High Distinction award.
The first problem in the Junior division is shown below:
J1 Annabel’s Ants
Annabel made a shape by placing identical square tiles in a frame as shown in the diagram below. The tiles are arranged in columns. Each column touches the base but no column touches the sides or top. There are no empty gaps between columns. The frame can be enlarged as needed
Annabel notices an ant walking along the edge of the shape made by the tiles. Beginning at the start, the ant follows the thick line. It walks a total of 11 tile edges to reach the finish.
a Show that it is possible to arrange seven tiles so that the ant walks exactly 8, 9, 10, 11, 12, 13, 14, 15 tile edges.
b Show six ways of arranging seven tiles so that the ant walks a total of nine tile edges.
c Show that is is possible to arrange 49 tiles so that the ant walks a total of less than 21 edges.
d Show four arrangements of 137 tiles, each arrangement with a different maximum height, so that the ant walks a total of 34 tile edges.
On Thursday 27 July, students throughout Australia and the Pacific will be sitting the Australian Mathematics Competition. At St Catherine’s School, all girls in Years 7 and 8 are entered and it is optional for students from Years 10, 11 and 12. (The Year 9 girls are not involved as they are on the H2H trip.) News of these results will follow later this term.