Category Archives: Grade 12

Data on IMO results

Following the recent IMO 2016, I have been meaning to do some analysis on IMO results. Unfortunately I have not had time to do so… In the meantime, I thought I’d share the data I’ve scraped so far so that … Continue reading

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IMO 2016

This year’s International Mathematical Olympiad (IMO) took place in Hong Kong from 6-16 July. The problems can be downloaded from this page or viewed at the Art of Problem Solving (AoPS) forum page for IMO 2016 (here). Congratulations to my country, … Continue reading

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[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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