Imp 2 Pow: Kick It

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Problem Statement: A football league scores points for field goals as five points and touchdowns as three points. They want to know what the highest amount of points that is impossible to score.

Process: I thought that maybe there was patterns in certain combinations.

Field goals = 5 pts. Then I listed the multiples of 5 to 25. 5,10,15,20,25
Touchdowns = 3 pts. I did the same as above.
3,6,9,12,15,18,21,24,27
I looked at the patterns and knew that if the team only scored field goals they would go up by 5 pts. each score. If the team only scored touchdowns they would go up by 3 pts. each score. I decided that I was going to keep looking for patterns in the numbers for different combanations ex. one field goal the rest touchdowns. To keep track of the patterns i was going to make a chart 1-100 of all the patterns and numbers.

12345678910
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899100

Touchdown rest Field Goals = 3,8,13,18,23,28,33
I noticed that one the digits got into the teens there was a pattern of hitting all the numbers ending with 3 and 8.

Field Goal rest Touchdowns = 5,8,11,14,17,20,23,26,29
This pattern is a little bit more tricky, but i noticed that its just like the threes it goes up three every number but instead of zero being the starting number it is five.

Two Touchdown rest Field Goals = 3,6,11,16,21,26,31
After three the pattern hits every number ending in 1 and 6

Two Field Goals rest Touchdowns = 5,10,13,16,19,22,25,28
Like the others that have rest touchdowns they go up by three this patter has a start of 10.

Three Touchdown rest Field Goals= 3,6,9,14,19,24, 29,
after the pattern reaches nine the pattern hits every number ending with 4 and 9.

Three Field Goals rest...
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