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.