Fay’s Nines Reflection

In fays nines we were required to make a vertical addition chart that equals 999. We had to make the number 999 with the digits 1 to 9 using vertical addition. You had to try to get all possible solutions with a rule that might help you with that.

At first I don’t think i under stood it very well because I thought you could just use 2 columns but then I found you had to use all 3 columns and all 9 numbers. After that I thought it was going to be a good challenge that we can explore well. I also started to try and use friends f ten at the start but then it just didn’t work, so i moved on.

I noticed that you can swap the numbers around to make unique solution which really helped in finding them all, I first thought there were 20 solutions in each one but after that I found out there were 36 in each solution. We later called these groups of solutions “sets.”

Well, I knew that you had to carry because carrying was very important in this project, I found out that the ones equalled 19, the tens equal 18 and the hundreds equals 8 so we carried the 10 from the units over to the ten, then from the 100 to the 100 that will equal 999. That’s how I broke the question down.

I found out why the max solutions is 180. So there is 36 unique solutions if you just find one solution, 36 is a multiple of 180 so that meant we just needed to find 5 different solutions to get 180. The reason there is 36 solutions in 1 solution is because you can change 1 column 6 times then you can change it again to get 18 and  then double it because of the other solution with the other solutions to get the total of 36 solutions.

I found the carrying the hardest because you are understanding it well but if you get distracted you just completely forget where you are up to then you have to start again, and it gets really frustrating but once you get an answer you feel good and like you deserved it. Getting started off was also another challenge because I didn’t really know how and what to do but once I got started off it was a really fun project.