Soccer Mania (part 2)
In the new season of the Clay's Bar Premier Soccer League, Mean City is destroying all comers. The teams still play 38 games total, with 3 points given for a win, 1 point for a tie, and 0 points for a loss.
Which of the given numbers is a point total Mean City CANNOT finish with at the end of the year?
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1 solution
The maximum possible point total for Mean City is 114 points (38 wins.)
If they tie a game, they lose 2 points from the maximum possible, and if they lose a game, they lose 3 points from the maximum possible.
So there is no way to finish just 1 point short of the maximum possible. 113 points in not achievable.
[Ways to achieve the other numbers given: 114 -- 38 wins, 112 -- 37 wins and 1 tie, 111 -- 37 wins and 1 loss, 110 -- 36 wins and 2 ties.]