NMBR140 assignment 2 1. In a radical and controversial change, designed to counter low scores, FIFA is changing the scoring of the World’s most popular game. Teams will soon get 8 points for a goal...

NMBR140 assignment 2
1. In a radical and controversial change, designed to counter low scores, FIFA is changing the scoring of the World’s most popular game. Teams will soon get 8 points for a goal and 5 points for a corner.
(a) What scores less than 100 are not possible for a team to get under this new system?
The total points would be of the form 8x+5y where x and y are strictly positive integers or 0.
The possible scores would be 0, 8, 16, 24…..96, 5,10,15,20….., and 13, 18, 21,…so on.
The scores would go as 0, 5, 8, 10, 13, …
i.e. all multiples of 5 or all multiples of 8 or all combinations of 8x+5y where x and y are integers.i.e.
Possible scores are 0,5,10, 15,…..100, 8, 16, 24, 32, 40,….96, and
13, 18, 23, 28, 33, 38, 43, 48, 53, 58, …….98 and
21, 29, 37, 45,……….98
When we group we get 0,5,8,10,13,15,18,20,23,24,……….
Thus we can say that not possible scores are the numbers not in...