George and Dominic from St Nicolas C of E Junior School sent us very clearly explained solutions to this problem. Thank you! Here is what they wrote for the first part:



1. For the first question I worked it out by seeing that number 3 was at 180∘ and that meant I needed to divide 180 by 3, giving the angle in between each number. The answer was 60∘ . By knowing this I could work out that number 2 was 120∘ away from zero anticlockwise and was 240∘ clockwise from zero.
2. To work this out I did almost the same as I did with question 1 except that I divided 180 by 4 instead. This gave me 45∘ between each number. By multiplying 45∘ by 3 (which is how many numbers 5 is away from zero ) I got 135∘ . This meant that I would have to either turn the dial 135∘ clockwise or 225∘ anticlockwise.
3. This was a little easier to work out because number 3 was a quarter of the way round the dial meaning to get to it I either had to turn it 90∘ anticlockwise or 270∘ clockwise.
4. This was harder than the previous questions because there wasn't a number at the 180∘ point. To work it out I divided 360∘ by 9. This gave me how many degrees I would have to turn the dial to get to the next number. The answer was 40∘ . This showed me that to get to number 3 I had to turn it either 120∘ anticlockwise or 240∘ clockwise.
5. At first sight this looked really tricky but after thinking about it wasn't. Number 12 is 180∘ away from zero. Half of 12 is 6 and half of 180 is 90, meaning that to get to the number 6 I have to either turn the dial 90∘ anticlockwise or 270∘ clockwise.

George and Dominic continued to explain how they had gone about the second part of the solution:


The next five were the hardest questions because we couldn't see where the zero was at the start.
A. For this question I worked out that 12 was 180∘ from zero and 180 divided by twelve is 15. This means that each section is 15∘ wide. There are 9 spaces between zero and nine which means that to work out the answer we have to times 9 by 15 which equals 135. So to get to 9 I have to turn the dial either 135∘ anticlockwise or 225∘ clockwise.
B/ We found this one quite easy because again 6 was a quarter of the way round, so this meant that we had to turn the dial 90∘ clockwise or 270∘ anticlockwise.
C/ First I worked out that 360 divided by 6 is 60 meaning that each section is 60∘ around the dial. Using this information I worked out that I would have to turn the dial either 120∘ clockwise or 240∘ anticlockwise.
D/ On this one I knew that 6 was at 180∘ but you had to work out what 5 was. So I did 180 divided by 6 which equals 30. Then I did 180-30 which equals 150∘ so it was 150∘ anticlockwise and 210∘ clockwise.
E/ Firstly for this I divided 360 by 9 which gave me 40. I then multiplied 40 by 5 which gave me 200. Knowing this I could work out that to get to 5 I either have to turn the dial 200∘ anticlockwise or 160∘ clockwise.

We ended the lesson by writing down 3 instructions for someone else to follow which would give our combination. Sophie, another girl in our group, wrote down: Using dial D, turn the dial 240∘ anticlockwise. Then from that point, turn the dial 210∘ clockwise. Then from this point, turn the dial 90∘ anticlockwise. What's my combination?
We worked out that it was 8 1 4.

Very well done to you both. You obviously worked hard on this activity. Thank you too, to Eve and Rachel from Castle Carrock Primary who also sent in well-explained solutions.