AMC8 2004

AMC8 2004 · Q18

AMC8 2004 · Q18. It mainly tests Casework, Logic puzzles.

Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers 1 through 10. Each throw hits the target in a region with a different value. The scores are: Alice 16 points, Ben 4 points, Cindy 7 points, Dave 11 points, and Ellen 17 points. Who hits the region worth 6 points?

五个朋友参加飞镖投掷比赛。每人投两支飞镖击中同一个圆形靶，每个人的得分是击中靶区得分的总和。靶区得分为1到10的整数。每支飞镖击中的区域得分不同。得分分别是：Alice 16分，Ben 4分，Cindy 7分，Dave 11分，Ellen 17分。谁击中了6分的区域？

(A) Alice Alice

(B) Ben Ben

(D) Dave Dave

(E) Ellen Ellen

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) Ben must hit 1 and 3. This means Cindy must hit 5 and 2, because she scores 7 using two different numbers, neither of which is 1 or 3. By similar reasoning, Alice hits 10 and 6, Dave hits 7 and 4, and Ellen hits 9 and 8. Alice hits the 6.

（A）Ben 必须击中 1 和 3。这意味着 Cindy 必须击中 5 和 2，因为她用两个不同的数字得到 7 分，而这两个数字都不是 1 或 3。用类似的推理，Alice 击中 10 和 6，Dave 击中 7 和 4，Ellen 击中 9 和 8。Alice 击中 6。

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