Sealed Solution
By Ellie in Year 5 at St. Nicolas CE Junior School, Newbury.
I found three solutions:
7 8 13 14 3
4 & 3 0 & 8 7 & 6 9 & 5 1 & 2
7 & 0 5 & 3 9 & 4 8 & 6 1 & 2
5 & 2 7 & 1 9 & 4 8 & 6 0 & 3
For my first solution, I started with the highest envelope (14) and I thought it made sense to start with the highest card – 9. The number that went with 9 to make 14 was 5, so I had made one pair. Then I did 13, the second highest. As I had already used 9, I tried 8. To go with 8 to make 13, I needed 5 but that had already been used. So I had to use 7 and 6.
Next, to make 7 from what was left, I had to use 3 and 4. Then 8 and 0 was perfect for 8 which left 1 and 2 for envelope 3 which worked. That was my first solution.
For my second solution, I tried a different solution for 14 which was 8 and 6. Then for 13 I had to use 9 and 4. There were two solutions to make 8 and this time I chose 5 and 3. Then 7 was made from 0 and 7 and 3 from 1 and 2 which all worked.
For my last solution, I used 8 and 6 for 14 again and 9 and 4 for 13. For 8 I used 7 and 1 which was different. To make 7, I used 5 and 2 (also different) and for 3, I used 0 and 3.
There were no other ways of making 14 so I knew I had found all the solutions.
So the numbers which could be inside the 8 envelope were 0 & 8, 5 & 3 or 7 & 1.