Difference between revisions of "2004 AMC 8 Problems/Problem 18"
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==Solution 1== | ==Solution 1== | ||
− | The only way to get Ben's score is with <math>1+3=4</math>. Cindy's score can be made of <math>3+4</math> or <math>2+5</math>, but since Ben already hit the <math>3</math>, Cindy hit <math>2+5=7</math>. | + | The only way to get Ben's score is with <math>1+3=4</math>. Cindy's score can be made of <math>3+4</math> or <math>2+5</math>, but since Ben already hit the <math>3</math>, Cindy hit <math>2+5=7</math>. Similarly, Dave's darts were in the region <math>4+7=11</math>. Lastly, because there is no <math>7</math> left, <math>\boxed{\textbf{(A)}\ \text{Alice}}</math> must have hit the regions <math>6+10=16</math> and Ellen <math>8+9=17</math>. |
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==Solution 2== | ==Solution 2== |
Revision as of 11:55, 12 October 2019
Contents
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?
Solution 1
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 .
Solution 2
Taking the 2 largest scores to narrow out the points we get
Ellen with either or and Alice with either or , the 2 pairs that work are Alice= Ellen=, therefore Alice scored the .
See Also
2004 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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