# 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.

# Win At The Fair

### Starting Point

At the start, I partnered up with ditch to play the losing game. In our class data it definitely showed that this game was loosing money, the main reason was that the minimum prize, 20c was at the top and the only numbers that would get it up there were 6,7 and 8, which makes it one of the lower chance ones to land on.

### The Problem

I wasn’t here for the problem but I tried my best to understand it. The main reason I think my game is enticing is that the top prize is \$400, and because the prize is so big it will distract the player from the chances, and if one of the players is smart enough to look at the chances he or she will see that you can role a 2 to go left (There is only one way to role a 2) and a 1 (For extra enticement even though it is impossible to role a 1) and a 12 to go right (There is also only 1 way to role a 12) and of course another 1 to go right for enticement.

### Official Board

For my official game board my tally of ten games turned out to be ok, I got 6 20c winners and 4 25c winners, which means the total that got put in to play was \$10, the total I had to give out was \$2.20, so the total I made was \$7.80. On the software in 1000 games, my best average per game was 22c, so that means on average every game I make 78c.

### Reflection

In one of the lessons my main goal was to find out which number on 2 dice has the least chance of being rolled. That’s were I got 2 and 12 from, and that’s what i think boosted my game. the other reason my game is quite enticing is that i actually showed my mum my game board and she said “I would definitely play your game zephy, but it is a bit of a gamble”. And I was looking at her eyes and not once did she look at the chances even though I mentioned it to her! As i said my average per game was 78 cents on the software, so that proves that my game will profit the school some money.