Five children play a game in which players either gain 1 point or lose 1 point. After several games, the number of points won is equalto the number of points lost. If no two children have the same final score and the overall winner has fewer points than the child with the lowest score lost, whaqt is the greatest possible lowest score?
Here "greatest" lowest score is interpreted to be the least negative score.
Constraints:
- sum of positive scores = sum of negative scores
- no two score is the same
So try 2,1,0,-1,-2
so that -2 is the least negative score.
what is rudeus
To find the greatest possible lowest score, we need to determine the range of possible scores and then identify the highest score in that range.
Let's assume the lowest score is x. Since there are 5 children, the highest score is (x+4) since no two children have the same final score.
Let's analyze the total points won and lost:
The total points won by all the children are (x+4) + (x+3) + (x+2) + (x+1) + x = 5x + 10.
The total points lost by all the children are x + (x+1) + (x+2) + (x+3) + (x+4) = 5x + 10.
Given that the total points won is equal to the total points lost, we have the equation:
5x + 10 = 5x + 10
This equation is true for any value of x, indicating that the value of x can be any real number. However, the question specifies that the overall winner has fewer points than the child with the lowest score lost. This means that the highest score cannot be equal to the lowest score lost.
Since the highest score is (x+4), and it cannot be equal to x (lowest score), we can conclude that the greatest possible lowest score is x = 0.
Therefore, the greatest possible lowest score is 0.