Archery

We've received some suggested settings for the sight and several of you told us that you did it by trial and error. Callum from Sompting Abbotts described his method:

I find that the best way to adjust the sight is to aim at the arrow that was fired last.

Several of you found settings that worked extremely well, but Adam from Dartford Grammar School came up with the most high-scoring solution:

For the key stage 3 archery maths challange I think that it's solution is: $x = 24$ $y = 34$.
I did this by a course of trial and error.


Well done Adam, that's very close to the solution we found of x = 25 and y = 33. Unfortunately nobody told us how they knew that their solution was the best one. The trick is, if you have hundreds of attempts with the correct settings you should gain an average score close to 9. So one way of improving your trial and error technique would be to fire about a hundred arrows, record the average score, and then change the setting and repeat the process. If the average goes up then you know you're heading in the right direction, but if it goes down then you know it's not right.

Why not try out the settings given here and see how they compare to the settings you found? Thanks for all your solutions, and we hope you enjoyed doing some maths Robin Hood style!