# Fay’s 9’s

Fay’s 9’s was a project maths problem involving vertical addition. Fay needed to make a vertical addition sum that would add up to 999. She had to find all the possible unique solutions. The catch was that she could only use the numbers 1 to 9 and no double ups. We know that there are 180 solutions because Leo spilled the beans. This was what it looked like…

After a little while my group (Lexi, Piper, Sophie Vo, Matisse, Poppy) and I discovered some patterns that involved the units column HAD to add up to 19, the tens column ALWAYS equalled 18 and the hundreds column NEEDED to make the sum of 8.

When playing with the problem we used the test all possibilities. We used this strategy when trying to find out all of the possible sums for 19, the units column. At first we came up with what we thought were 28 unique sums for 19, by switching different combinations for example…

2+8+9

2+9+8

8+2+9

8+9+2

9+2+8

9+8+2

We thought that they were all unique but really only one is unique. In the end there were only 5 different combinations.

My group broke this problem into manageable parts by doing what I explained in the previous paragraph. By breaking the problem up we discovered that 36 had a big role to play in this problem. We played around with the different combinations to do with the 5 different solutions we found for 19.

As far as we got into the investigation was coming up with this worded problem…

There are 5 different combinations that equal 19. You can swap the tens and hundreds columns around 6 times.

6×6=36

36×5=180

6x6x5=180

There are 180 solutions.

This project was challenging because there were lots of small problems in the one big problem. You had to solve multiple different sums at the same time. I also wasn’t expeirenced with vertical addition so I was learning more then one thing at a time. It was hard to decide which combinations were unique and which ones were the double ups. I think it would have been harder if we didn’t know there were 180 unique solutions.