# 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.

# Win At The Fair

The starting point of win at the fair was to test out the original game board. To profit money we would have to win at least \$300 for our school if we played it 1000 times, considering our \$1 entry fee this was quite hard because no one has the time to play 1000 times. As a class our end total money going in was\$104 and going out was \$152.60. That meant we lost \$48.60 for our school.

This had a non-profitable ending and I wouldn’t go up to it at a fair because the prices aren’t enticing.

If we were expected to make over \$300 out of \$1000 we would need to lower some prices and change the directions of some of the numbers that were easy to roll. We collected up some ideas to improve the original game board to build our creative boards.

Some of these ideas weren’t possible because the computer software maths 300 (more on that later) wouldn’t allow things like snakes and ladders or obstacles and black holes.

I put together my creative game board and changed the majority of the board. We could do anything with this board but if we didn’t profit from it, it was useless. I wanted it to be enticing and profitable…

The two first hexagons to the left and right of the hexagon are \$0.50 so that you only have one chance to move to a different hexagon because it was a \$2 playing fee the school makes \$1.50 every time they land on those to hexagons.

These are the numbers i changed from the original game board to the creative…

\$5 = \$10

\$4 = \$2

\$3 = \$1

\$2 = \$1

\$1 = \$0.50

\$0,50 = \$0.20

\$0.20 = \$0.5

I also changed the directions of all the numbers…

2 & 3 = top left

4 & 5 = up

6 & 7 = top right

8 & 9= bottom left

10 & 11 = bottom right

12 = down

This didn’t really work how I wanted it to because before you get onto the actual game board and you would go all around but not win anything unless you went left or right on your first roll. My game board did profit for the school but it wasn’t very practical.

In = \$20

Out = \$7.50

Profit = \$12.50

What I needed to change:

• how the numbers go down because it took so long before the actual game board.
• the 2 \$0.50 got 9/10 times, if customers saw that they probably wouldn’t play if they were going to lose \$1.50
• the game appeal using the numbers on the side

My official game board couldn’t have the two \$0.50 next to the starting hexagon because of how the computer software was set out. My entry fee has to be \$1.

For my official game board I was thinking more strategical, so I put 12 going to the left, 2 & 3 to the right and 4,5,6,7,8,9,10&11 going straight. This meant that they didn’t have much chance of getting the highest price. 12 & 2 both only have one chance to be rolled and the 3 is there for more enticement. This list shows the prize money amounts from top to bottom…

50c

\$1

25c

50c

20c

\$100

\$200

The enticement of my board is quite strong because I know if I had a chance of winning \$200 with only paying \$1 to play I would definitely play. I thought I would make more money for my school because it’s hard to roll the same number 3 times. I played my game 10 times…

In = \$10

Out = \$4.20

Profit = \$5.80

When I was up to the software I thought that because no one won \$100 or \$200 I would change them to \$1000 and \$100. This is what happened when I tested my game bored 4000 times.

After I played this I thought if someone was to play it and win the big jackpot of \$1000 then my school would automatically lose a lot of money. I decided to change a few of the prices to still make it enticing but still keeping the rolls the same. This is how it turned out…

Overall I think all my game boards were inciting and I profited over \$300 for my school every time. This project taught me that it’s not all about how the customer thinks because if the game doesn’t help the school it’s pointless.