# Fay’s Nines Reflection

** Fay’s Nines with vertical addition problem with numbers 1-9 to equal 999. There are 180 solutions to equal 999 from numbers 1-9, we have to try to find a way to find them all. We were told how many there were so we had to work backwards. **

**When we started to work with this problem I was a bit confused what the end aim was so I just started to make some vertical addition problems and try and find as many as I can**

**, some of the patterns I noticed were only 1-5 cold be in the hundreds section, the ones section had to equal 19, the tens section had to equal 18 and the hundreds section had to equal 8 this is because we at doing vertical addition and we have to carry numbers. Some other patterns I found were if you found one solution you could swap numbers to make a unique solution, you could do this 36 without putting numbers in different sections. **

**To break this problem into manageable parts I found one solution and tried to find as many unique solutions without changing the section the numbers are in. I found there are 36 in each one.**

**We did get to 180 but we needed to prove that you can find 36 in each ‘set’ as we called them, we found 5 ‘sets’ and 5×36 equals 180 but we didn’t get to prove that.**

**This project was challenging because I didn’t understand it that well, I only got what we had to do in the very last session and that is when I found 36 is in each ‘set’. The main challenge for me was that you had to do it all manually, like you had to write down every solution and there was no specific rule.**