Problem statement: In the Kick it POW we are being asked to find the highest impossible score when field goals are worth 5 points and touchdowns are 3 points. The final score can be any combination of touchdowns and field goals. After doing that the problem asks for us to make our own scoring system using whole numbers. The final task is to come up with other situations that include impossible scores and state what pattern can be seen between the different situations.
Process: I tried to create a chart of all the multiples of 5 and 3. A classmate suggested using 5 as a ladder to larger numbers before using 3’s. So to make things easier for myself I wrote how the numbers would work. I began at seven and went up to 30.
The equation xy-(x-y) was discovered to find the highest impossible score by someone else. After a bit of thinking I found that the equation was of no use because 7 was confirmed to be the highest impossible number. Also I couldn’t quite figure out why it works so I decided to omit it.…show more content… Multiples of 2
Scores
P=possible I= impossible
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
I
P
The odd numbers were impossible because every combination will always end up being an even number.
Another scoring system would be 2 and 3.
Multiples of 2
Multiples of 3
Scores
I/P
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
3
6
9
12
15
18
21
24
27
30
33
36
39
32
35
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
I
2 (P)
3 (P)
2+2 (P)
3+2 (P)
3+3 (P)
2(2) + 3 (P)
2(4) (P)
3(3) (P)
2(5) (P)
3(3) + 2 (P)
3(4) (P)
2(5) + 3
