Tag Archives: AIME

[Soln] 2013 AIME I Problem 15

2013 AIME I 15. Let  be the number of ordered triples  of integers satisfying the conditions (a) , (b) there exist integers , , and , and prime where , (c) divides , , and , and (d) each ordered triple … Continue reading

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2013 AIME I Problem 15

2013 AIME I 15. Let  be the number of ordered triples  of integers satisfying the conditions (a) , (b) there exist integers , , and , and prime where , (c) divides , , and , and (d) each ordered triple … Continue reading

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[Soln] 2013 AIME I Problem 14

2013 AIME I 14. For , let and so that . Then where and are relatively prime positive integers. Find .

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2013 AIME I Problem 14

2013 AIME I 14. For , let and so that . Then where and are relatively prime positive integers. Find .

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[Soln] 2013 AIME I Problem 13

2013 AIME I 13. Triangle has side lengths , , . For each positive integer , points  and are located on  and  respectively, creating three similar triangles . The area of the union of all triangles  for  can be expressed as , where  and  are relatively prime … Continue reading

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2013 AIME I Problem 13

2013 AIME I 13. Triangle has side lengths , , . For each positive integer , points  and are located on  and  respectively, creating three similar triangles . The area of the union of all triangles  for  can be expressed as , where  and  are relatively prime … Continue reading

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[Soln] 2013 AIME I Problem 12

2013 AIME I 12. Let  be a triangle with  and . A regular hexagon  with side length 1 is drawn inside  so that side  lies on , side  lies on , and one of the remaining vertices lies on . There are … Continue reading

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