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jmc

number theory junior

Problem

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 through . Each throw hits the target in a region with a different value. The scores are: Alice points, Ben points, Cindy points, Dave points, and Ellen points. Who hits the region worth points?
(A)
(B)
(C)
(D)
Solution
The only way to get Ben's score is with . Cindy's score can be made of or , but since Ben already hit the , Cindy hit . Similarly, Dave's darts were in the region . Lastly, because there is no left, must have hit the regions and Ellen .
Final answer
A