The second question was a classic geometry problem involving circles and triangles, using a number of circle theorems and spotting similar and congruent triangles. Unsurprisingly, having a good diagram was essential to finding and writing a good solution. I noticed that there were a number of different solutions, all equally valid but some much more elegant than others. Having written a fairly convoluted solution, I noticed from my diagram that a far simpler solution was possible and the published solution is different still. That is normally the fun with geometry questions!
The writers were keen on combinatorics this year with the last three questions all some sort of counting problem. The fourth question was about ways of painting 100 houses in a row in two colours. The second part was deceptive, leading us to think there were far fewer possible arrangements than there really were and culminating in most of us making the same error. Listing arrangements systematically was essential.
The final question, which was about a game involving coins arranged on a chequered square board, was cumbersome and I’m still not entirely sure why the last part was the same number of marks as the previous part (as it was completely dependent on trial and error and spotting an arrangement that worked), nor have I since found a more sensible way of approaching it… all I can say is hats off to everyone who persevered to find a solution.
As always, this year’s MOG was really fun, and not just because it went better than previous years and we got to miss lessons. I would highly recommend that keen mathematicians should have a go next year!
Heeral, Year 13