Tag Archives: 2013

[Soln] 2013 AIME I Problem 15

Posted on 18 Jun 2016 by kjytay

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 →

Posted in Grade 12, USA | Tagged , , | Leave a comment

2013 AIME I Problem 15

Posted on 18 Jun 2016 by kjytay

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 →

Posted in Grade 12, USA | Tagged , , | Leave a comment

[Soln] 2013 AIME I Problem 14

Posted on 17 Jun 2016 by kjytay

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

Posted in Grade 12, USA | Tagged , , | Leave a comment

2013 AIME I Problem 14

Posted on 17 Jun 2016 by kjytay

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

Posted in Grade 12, USA | Tagged , , | Leave a comment

[Soln] 2013 AIME I Problem 13

Posted on 16 Jun 2016 by kjytay

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 →

Posted in Grade 12, USA | Tagged , , | Leave a comment

2013 AIME I Problem 13

Posted on 16 Jun 2016 by kjytay

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 →

Posted in Grade 12, USA | Tagged , , | Leave a comment

[Soln] 2013 AIME I Problem 12

Posted on 15 Jun 2016 by kjytay

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 →

Posted in Grade 12, USA | Tagged , , | Leave a comment

2013 AIME I Problem 12

Posted on 15 Jun 2016 by kjytay

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 →

Posted in Grade 12, USA | Tagged , , | Leave a comment

[Soln] 2013 AIME I Problem 11

Posted on 14 Jun 2016 by kjytay

2013 AIME I 11. Ms. Math’s kindergarten class has 16 registered students. The classroom has a very large number, , of play blocks which satisfies the conditions: (a) If 16, 15, or 14 students are present, then in each case all the blocks … Continue reading →

Posted in Grade 12, USA | Tagged , , | Leave a comment

2013 AIME I Problem 11

Posted on 14 Jun 2016 by kjytay

2013 AIME I 11. Ms. Math’s kindergarten class has 16 registered students. The classroom has a very large number, , of play blocks which satisfies the conditions: (a) If 16, 15, or 14 students are present, then in each case all the blocks … Continue reading →

Posted in Grade 12, USA | Tagged , , | Leave a comment