Fay’s Nines is using the number 1-9 in vertical addition problem. It has to add up too 999. It has 3 columns of the number 1-9. There are lots of different ways to make 999 using all the numbers 1-9 only once.
When we first started this I thought it would be much easier to find number that added up to 9, but I found out that it is a lot harder. Once I found a bit of a pattern to get some answers it started to get a lot easier. I found that you cant keep making 9 out of all the numbers so what I did was make 19 for the first column then make the next on 18 because you carry the 1 then the next column you make 8 because you carry the 1 again.
I found on the end column had to add to 19 then the next 18 because you carry the 1 then the last column add to 8 because you carry the 1 from the 18. After I did that I found that I can use 10 factors. For example
5 4 3
1 8 7
2 6 7
9 9 9
You carry the one from the 19 then you also carry the one from the 18.
How I first broke up this problem was that I tried to find at least 1 solution too work off that, once I found a couple if solutions I used them and I tired to see if I can find any patterns. Once I found a small pattern I tried to find all the 180 solutions.
I didn’t find all the solutions I didn’t find heaps but I realised I could change the number around a fair bit so I mixed the number around. I found a couple of patterns and a fair few solutions. If I had another session I would try to find a way to find all the solutions.
Because at the start I didn’t realise you need to carry the numbers. It also took me a little while to find a pattern and I didn’t end up finding a rule.