Kick it
Problem Statement: The football League has to do things different. They are not scoring their games how everyone does. They thought of a scoring system:
Each field goal counts for 5 points
Each touchdown counts for 3 points.
The only way is to combine the field goals and the touchdowns somehow. Every score is not possible in their league. A score of 1 point isn’t possible, neither is 2 or 4. The task is to find out what is the highest impossible number you can’t make and explain how you for sure.
Process
- The first thing that I tried was making a list from 1 to 20. I checked and put x’s by the numbers you can make and numbers you cannot. This was pretty difficult for me to understand because I did not know what they were really asking me to do. I worked with some friends and they showed me how I can start. My teachers helped me by making sure I understand what was going on with the football league. I also made other scoring systems such as (2,7) and (3,9).
The highest number impossible for 2 and 7 is 5. I stop at 20 and from 1 to 20 the highest number impossible was 5. Every other number except for 1, 3, and 5 were checked. The highest number for 3 and 9 is 20. I also stop at 20 from 1. I think these numbers were the highest impossible numbers because they did not have any other numbers that can make that number equal.
Solutions- The highest number impossible is 7. I truly think its 7 because you cannot score 7 with either a 3 or a 5. Also I believe that the higher number is possible because they can all have numbers that can equal to them with no problem because they are getting larger. The pattern I saw when I was doing the points 5 and 3, and other scoring systems were the higher the number is the more possible numbers. I found that certain numbers can be impossible in 2 digits numbers and being higher because of the 2 number you picked. Self Assessment- I think I deserve a B because I tried my best to work this out even know I didn’t
Each field goal counts for 5 points
Each touchdown counts for 3 points.
The only way is to combine the field goals and the touchdowns somehow. Every score is not possible in their league. A score of 1 point isn’t possible, neither is 2 or 4. The task is to find out what is the highest impossible number you can’t make and explain how you for sure.
Process
- The first thing that I tried was making a list from 1 to 20. I checked and put x’s by the numbers you can make and numbers you cannot. This was pretty difficult for me to understand because I did not know what they were really asking me to do. I worked with some friends and they showed me how I can start. My teachers helped me by making sure I understand what was going on with the football league. I also made other scoring systems such as (2,7) and (3,9).
The highest number impossible for 2 and 7 is 5. I stop at 20 and from 1 to 20 the highest number impossible was 5. Every other number except for 1, 3, and 5 were checked. The highest number for 3 and 9 is 20. I also stop at 20 from 1. I think these numbers were the highest impossible numbers because they did not have any other numbers that can make that number equal.
Solutions- The highest number impossible is 7. I truly think its 7 because you cannot score 7 with either a 3 or a 5. Also I believe that the higher number is possible because they can all have numbers that can equal to them with no problem because they are getting larger. The pattern I saw when I was doing the points 5 and 3, and other scoring systems were the higher the number is the more possible numbers. I found that certain numbers can be impossible in 2 digits numbers and being higher because of the 2 number you picked. Self Assessment- I think I deserve a B because I tried my best to work this out even know I didn’t