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Arf League

Who is Cahit Arf? What is Arf League?
Cahit Arf (11 October 1910 â€“ 26 December 1997) was a Turkish mathematician. He is known for the Arf invariant of a quadratic form in characteristic 2 (applied in knot theory and surgery theory) in topology, the Hasseâ€“Arf theorem in ramification theory, Arf semigroups, and Arf rings. For more information please check Wikipedia.
Arf League is for enthusiasts who seeks challenging math problems. Please feel free to send your solutions or general comments to challengingproblems@ahmath.com.

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✔ There are 119 problems and 82 key facts, waiting for math enthusiasts! Dear Math Enthusiasts,
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Format of the items of the selection menu: Problem Order, Problem Code (Difficulty Level). Red problems have a difficulty level of less than 0.75, thus, as an example, a 0.18 means only 18% of all answers submitted are correct.
Futured Math Enthusiasts
is solved firstly by
Mohamed Karamany
D146
by Fujiwara Toneri
Long Jumper
Marathon Runner
6875
Score Table  Math Enthusiasts (only the first 100)
Score depends on number of correct answers and number of trials.
 FS stands for First Solver. For each problem, there is a first solver. Each time you solve a problem as the first person your FS score increases by one.
 SF stands for Solution Files. Some of the Math Enthusiasts sends solutions to the problems. This is to promote their valuable contribution to the Arf League.
 SP stands for Sniper. You can get this badge if and only if you do not miss any problem in your first try and solve them correctly. Only snipers have the potential to get the full score.
 UT stands for User Type. "MT" is for Math Teacher and "S" is for Student.
hide this Please submit your country to be listed in this table!
Order  Score  # of Correct Answers  Names  Badges  Country  

FS  SF  SP  UT  
1.  074.88  116  Caed Mark Medul Mendoza  17  111  MT  Philippines  
2.  073.27  101  Lee csek  0  1  China  
3.  066.27  91  Isaiah James de Dios Maling  4  27  MT  Philippines  
4.  065.25  92  Jeffrey Robles  17  5  Philippines  
5.  064.83  109  Angelo Velasquez  2  62  S  Philippines  
6.  057.83  92  Richard Phillip Dimaala Fernandez  4  90  MT  Philippines  
7.  056.30  67  Lilanie Monique Torilla  0  55  ❂  S  Philippines 
8.  055.42  84  Jereco Dela Pena  0  0  MT  Philippines  
9.  054.29  92  Reygan Dionisio  4  2  MT  Philippines  
10.  049.82  68  Amirul Faiz Abdul Muthalib  15  0  MT  Malaysia  
11.  049.63  61  Sumet Ketsri  5  63  Thailand  
12.  045.50  62  Kurara Chibana  6  0  S  Japan  
13.  045.38  54  Willie Revillame Wowowin  0  0  ❂  Philippines  
14.  045.07  63  Russel J. Galanido  2  30  S  South Korea  
15.  039.79  66  Mertkan Simsek  9  0  MT  Turkey  
16.  038.90  54  Marvin Cato  1  30  MT  Philippines  
17.  036.68  49  Radu Bogo  0  40  Romania  
18.  033.91  52  Law Tik Shun  0  0  MT  Hong Kong  
19.  031.74  48  Nixon Balandra  2  46  MT  Philippines  
20.  031.42  54  Randy Orton  6  0  United States of America  
21.  031.19  60  Rindell Mabunga  1  31  S  Philippines  
22.  030.73  48  Arcy Leann  0  8  S  Philippines  
23.  029.41  35  Arjun Singh Rajawat  0  4  ❂  S  India 
24.  028.25  41  Jacob Sabido  0  5  S  Philippines  
25.  025.23  41  Darwin Ojera  0  22  MT  Philippines  
26.  024.71  42  Fujiwara Toneri  0  3  S  Japan  
27.  023.16  41  Joselito Torculas  3  26  Philippines  
28.  022.38  57  Roenz Joshlee Timbol  0  1  S  Philippines  
29.  022.23  36  Lim Jing Ren  0  0  S  Malaysia  
30.  021.85  26  Alea Astrea  0  0  ❂  S  Philippines 
31.  018.94  26  Kuba Helsztynski  0  0  MT  Poland  
32.  015.97  19  Lenard Guillermo  0  2  ❂  S  Philippines 
33.  015.28  20  Gluttony  0  0  Philippines  
34.  014.72  29  Joseph Rodelas  1  0  S  Philippines  
35.  014.01  20  Mark Alvero  0  0  MT  Philippines  
36.  013.86  26  Norwyn Nicholson Kah  0  38  S  Philippines  
37.  013.82  25  Jhepoy Dizon  0  0  S  Philippines  
38.  013.04  32  Daniel James Molina  0  1  S  Philippines  
39.  012.45  20  Ralph Macarasig  0  0  S  Philippines  
40.  011.83  26  Joem Canciller  0  0  Philippines  
41.  011.76  14  John Albert A. Reyes  0  6  ❂  S  Philippines 
42.  011.04  17  Nheil Ignacio  0  8  S  Philippines  
43.  010.70  22  Hanelet Santos  0  15  S  Philippines  
44.  010.58  23  Kumar Ayush  0  1  S  India  
45.  010.14  28  Mark Kenneth Dairo  0  26  S  Philippines  
46.  010.12  17  Ibrahim Demir  0  1  MT  Turkey  
47.  009.72  18  Francis Gerard Magtibay  0  0  S  Philippines  
48.  009.24  11  Melga Sonio  0  0  ❂  S  Philippines 
49.  007.72  21  Christian Daang  1  25  S  Philippines  
50.  007.49  14  Angelu G. Leynes  1  0  S  Philippines  
51.  007.26  11  Mark Elis Espiridion  0  0  Philippines  
52.  006.46  13  Chris Norman Algo  0  10  S  Philippines  
53.  006.05  12  Charles Dwight M. Pelaez  0  8  S  Philippines  
54.  005.88  7  Adrian Pilotos Burgos  0  0  ❂  Philippines  
55.  005.66  16  CK Alexis Balidoy  0  1  S  Philippines  
56.  005.04  6  Yavuz Selim Koseoglu  2  0  ❂  S  Turkey 
57.  005.04  6  Mahmut Cemrek  0  0  ❂  Turkey  
58.  005.04  6  John Gamal Aziz Attia  2  1  ❂  S  Egypt 
59.  005.04  6  Jade N. Mijares  0  0  ❂  S  Philippines 
60.  003.36  6  Kevin Durant  1  0  S  Turkey  
61.  003.36  6  John Lester Tan  0  0  S  Philippines  
62.  003.36  4  Βαρελάς Γεώρ𝛾ιος  0  0  ❂  Greece  
63.  003.00  5  Kot Behemot  0  0  MT  United States of America  
64.  002.52  3  Gerald M. Pascua  0  0  ❂  Philippines  
65.  002.10  5  Leandro Dar Juan  0  0  S  Philippines  
66.  001.68  2  James Harden  0  0  ❂  S  Philippines 
67.  001.51  3  John Kenneth Vito Cruz  0  0  S  Philippines  
68.  000.84  3  wow magic  0  0  S  Philippines  
69.  000.84  1  Suleyman Akarsu  0  0  ❂  Turkey  
70.  000.84  1  Serkan Callioglu  0  0  ❂  Turkey  
71.  000.84  1  Ryan Magdayo Caduyac  0  0  ❂  S  Philippines 
72.  000.84  1  Rafael Zamora  0  0  ❂  S  Philippines 
73.  000.84  1  Mohamed Karamany  1  0  ❂  Egypt  
74.  000.84  1  Evan Phillip Mendoza  0  0  ❂  S  Philippines 
75.  000.42  1  Miguel  0  0  S  Philippines  
76.  000.42  1  Adnan Donmez  0  0  MT  Turkey  
77.  000.28  1  Jay Cyril Mijares  0  0  Philippines 
hide this All problems are solved 2459 times.
Score Table  Countries
Country  # of Correct Answers  # of Trials  Performance 

Hong Kong  53  68  77.94% 
Philippines  1832  2678  68.41% 
Turkey  110  155  70.97% 
India  143  331  43.2% 
Egypt  7  7  100% 
Thailand  83  103  80.58% 
Greece  4  4  100% 
Malaysia  104  127  81.89% 
Japan  160  352  45.45% 
South Korea  63  74  85.14% 
Romania  51  60  85% 
United States of America  71  104  68.27% 
Poland  26  30  86.67% 
China  101  117  86.32% 
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Worked Solutions to the Problems
Solutions to all Challenging Math Problems are ready!
If you want to get the pdf of all the questions with solutions please do the payment by using the paypal button given on the left. For more documents and info about olympiads, please click Olympiads.
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Key Facts

1. Key Fact Tags: product,rational,number,irrational

2. Key Fact Tags: fraction,lowest term,numerator,denominator,relatively prime

3. Key Fact Tags: square,even,integer,divisibility

4. Key Fact Tags: square,odd,integer,divisibility

5. Key Fact Tags: product,perfect square,consecutive numbers

6. Key Fact Tags: divisibility

7. Key Fact Tags: identity,factorial

8. Key Fact Tags: identity

9. Key Fact Tags: identity

10. Key Fact Tags: identity

11. Key Fact Tags: factorial,inequality

12. Key Fact Tags: identity

13. Key Fact Tags: identity

14. Key Fact Tags: SophieGermain,identity

15. Key Fact Tags: identity

16. Key Fact Tags: identity,factorization

17. Key Fact Tags: identity,factorization

18. Key Fact Tags: identity

19. Key Fact Tags: composite number

20. Key Fact Tags: prime number,definition

21. Key Fact Tags: prime number,composite number,1

22. Key Fact Tags: prime number,composite number,1

23. Key Fact Tags: prime number,even

24. Key Fact Tags: prime number

25. Key Fact Tags: prime numbers

26. Key Fact Tags: prime factorization

27. Key Fact Tags: prime number,composite number

28. Key Fact Tags: Wilson&#39;s Theorem

29. Key Fact Tags: Bertrand&#39;s Postulate,prime number

30. Key Fact Tags: Bonse&#39;s Inequality,prime numbers

31. Key Fact Tags: prime,divisor

32. Key Fact Tags: divisibility,square,odd,integer

33. Key Fact Tags: divisibility

34. Key Fact Tags: divisibility

35. Key Fact Tags: product,consecutive,integer,divisibility

36. Key Fact Tags: divisibility

37. Key Fact Tags: binomial expansion

38. Key Fact Tags: binomial expansion,number of terms

39. Key Fact Tags: identity

40. Key Fact Tags: identity

41. Key Fact Tags: identity

42. Key Fact Tags: identity

43. Key Fact Tags: identity

44. Key Fact Tags: chessboard,square

45. Key Fact Tags: arithmetic mean,real numbers

46. Key Fact Tags: geometric mean,real numbers

47. Key Fact Tags: arithmetic mean,geometric mean,inequality

48. Key Fact Tags: harmonic mean,real numbers

49. Key Fact Tags: arithmetic mean,harmonic mean,inequality

50. Key Fact Tags: inequality

51. Key Fact Tags: inequality

52. Key Fact Tags: inequality

53. Key Fact Tags: inequality,identity

54. Key Fact Tags: inequality

55. Key Fact Tags: inequality

56. Key Fact Tags: inequality

57. Key Fact Tags: inequality

58. Key Fact Tags: inequality

59. Key Fact Tags: inequality,identity

60. Key Fact Tags: Cauchy–Schwarz,inequality

61. Key Fact Tags: Chebyshev,inequality

62. Key Fact Tags: line,intersection,parabola,abscissa,vertex,midpoint,line segment

63. Key Fact Tags: De Moivre,formula

64. Key Fact Tags: fibonacci,numbers

65. Key Fact Tags: finite serie,finite sequence

66. Key Fact Tags: infinite serie,infinite sequence

67. Key Fact Tags: partial sum,series

68. Key Fact Tags: sequence,partial sum,series,limit

69. Key Fact Tags: sequence,partial sum,series,limit

70. Key Fact Tags: series,sum

71. Key Fact Tags: sum,infinite serie

72. Key Fact Tags: relative error,measurement

73. Key Fact Tags: angle,bisector,triangle

74. Key Fact Tags: sum,exterior angles,convex,polygon

75. Key Fact Tags: triangle,circle,greatest area,isosceles triangle

76. Key Fact Tags: circle,plane,common tangent

77. Key Fact Tags: lattice points,gcd,greatest common divisor

78. Key Fact Tags: right triangle,median

79. Key Fact Tags: minimal polynomial

80. Key Fact Tags: british flag theorem, rectangle, geometry

81. Key Fact Tags: pythagorean triple, triangle

82. Key Fact Tags: primitive pythagorean triples, triangle
If you want to be a contractor (problem writer, key fact writer, etc.), please contact AhMath by sending an email to challengingproblems@ahmath.com.
Amirul Faiz Abdul Muthalib
Problem Writer
Number of problems: 10With over 5 years of handson, successful teaching experience, Amirul is an enthusiastic PreUniversity Mathematics Lecturer in INTEC Education College, Malaysia. Being a versatile individual who love Maths, he has earned a Masterâ€™s Degree in Mechanical Engineering in Japan. He had opportunity to teach Maths in Japanese Syllabus for scholarship sponsored students who will further their study in KOSEN (National College of Technology in Japan). He also train some of his students for the National Olympiad every year.
Ä°hsan YÃ¼cel
Problem Writer
Number of problems: 3Ihsan is currently in the thesis phase of his postgraduate education, which is about mathematics teaching education. He got some notable national and international achievements in various secondary school mathematics and project competitions. Likewise, his students also got many elementary and secondary level mathematical olympics achievements. In the recent past, his students got the first and the second place in the TÃœBÄ°TAK National Secondary School Research Projects Contest. One of his students, a team member of the national math team, received a bronze medal in IMO. Heâ€™s an author of many scientific articles about mathematics in the quarterly magazine "Mathematical World". Heâ€™s the founder of Matematik MeraklÄ±sÄ±, a website dedicated to Mathematics.
Richard Phillip Dimaala Fernandez
Problem Writer
Number of problems: 1Richard is an experienced math teacher in a Chinese school in the Philippines. He is a product of Philippine Normal University (National Center for Teacher Excellence). He trains students who compete in both local and international math competitions. He is a trainer in Mathematics Trainers' Guild, Philippines (MTG Philippines) and MetrobankMTAPDepEd Math Challenge (MMC). He is also a lecturer in one of the review centers specialized in university entrance examinations. He is also a Suken Test Passer (Mathematics Certification Institute of Japan).
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It's a good way to practice maths and also the site encourages you to submit your answer with an accompanying solution. Participants can not just simply guess the answer or predict what will be the answer based on the given, they need to know and understand the topic. Also this refrains participants to just simply ask the answer from other people. So the method was excellent and people will definitely learn many things about math.
 Rindell Mabunga / Philippines
I want to say my deepest gratitude in creating this website. The questions are not the typical type and not normally taught to nonmathematical major degrees. I really hope that you'll continue your mission and vision in creating this site, as this serves as a platform to enhance our mathematical skills. Hoping for the best good luck!!!
 Russel J. Galanido / South Korea
I see AhMath as the one encouraging selfpaced learning or practice in solving math problems. It does not put me into any kind of pressure like requiring myself to be the first one to solve the problems correctly and giving answers with a limited time. Also, it gives me excitement for the next problems to solve as well as for the appearance of my name on the list of the people who submitted the correct solutions and answers for those math problems. Overall, it gives me confidence to be better in math.
Thank you for everything, AhMath. Marvin Cato / Philippines
I knew AhMath from a facebook group, "Math Enthusiasts Quiz Group", that I just joined a few weeks ago. Then I found that there are the "challenging math problems" here that refresh my Math skill.
I like many ideas on this website, the word "Math Enthusiasts" exactly describes what I'm and it makes me recall the feeling about Math when I was young, it was fun and exciting!
I like the motto "Real than i, rational than n", it's playing in my head and I'm still doubt about its meaning :D
There is no time constraint for solving the problems so we can think about the solutions in the different ways. Sometimes the new solutions reveal the beauty of Math and that only happens when we have time to think about other solutions.
Thank you the creator and moderator of this website, especially Ahmet Arduc, who brings me back to the feeling of fun and exciting with his creative problems. Sumet Ketsri / Thailand
Ahmath is basically a great site. The problems are really challenging and mind boggling. I really like the way that the Math enthusiasts should show the solution as well for each problem. You need to learn on your own. This site greatly help me improve my Math skills and writing solutions as well. Thank you much Ahmath for an amazing job. More power and God bless. "Train HARD, win EASY. Train Easy, win HARD". Hoping you all the best out there. Just continue on your aim to help the students as well as the nonstudents to further enhance their math skills. God bless and More power AHMATH FTW!!!
 Isaiah James de Dios Maling / Philippines
I want to thank sir Ahmet Arduc for creating this wonderful site AhMath. The "Challenging Math Problems" are really challenging. Most of the problems are math problems that you can't normally encounter in school. You can solve the problems in different ways. You can find some beautiful patterns while solving these problems. The problems are addictive especially the problems created by sir Ahmet. It brings me back the way i feel when i was young, the excitement and having fun when solving math problems. I'm always excited to see my name on the list of people who solved the problem correctly! I can say that I am really a Math Enthusiast now and I improved a lot with my mathematical skills. I also like that there is no time limit in solving the problems. You can solve the problems when you are not busy or you are in the mood to solve. Thank you Ahmath, I hope you'll continue to improve this site and help us to be better. Hoping you all the best, God bless!
 Caed Mark Medul Mendoza / Philippines