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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 126 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
9414
by Angelo Velasquez
Long Jumper
Marathon Runner
since 11.11.2019
10642
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!
Jay LeeOrder  Score  # of Correct Answers  Names  Badges  Country  

FS  SF  SP  UT  
1.  084.76  116  Zhuo Qun Song  0  2  S  Canada  
2.  082.47  118  Lee Csek  0  1  China  
3.  079.59  121  Daryll Ko  0  0  S  Philippines  
4.  075.04  123  Caed Mark Medul Mendoza  20  112  MT  Philippines  
5.  073.87  107  Isaiah James de Dios Maling  4  27  MT  Philippines  
6.  068.11  119  Angelo Velasquez  2  62  S  Philippines  
7.  062.40  93  Jeffrey Robles  18  5  Philippines  
8.  056.37  99  Reygan Dionisio  6  2  MT  Philippines  
9.  054.61  92  Richard Phillip Dimaala Fernandez  4  90  MT  Philippines  
10.  053.17  67  Lilanie Monique Torilla  0  55  ❂  S  Philippines 
11.  052.34  84  Jereco Dela Pena  0  0  MT  Philippines  
12.  047.05  68  Amirul Faiz Abdul Muthalib  15  0  MT  Malaysia  
13.  046.88  61  Sumet Ketsri  5  63  Thailand  
14.  042.97  62  Kurara Chibana  6  0  S  Japan  
15.  042.86  54  Willie Revillame Wowowin  0  0  ❂  Philippines  
16.  042.57  63  Russel J. Galanido  2  30  S  South Korea  
17.  037.58  66  Mertkan Simsek  9  0  MT  Turkey  
18.  036.73  54  Marvin Cato  1  30  MT  Philippines  
19.  034.65  49  Radu Bogo  0  40  Romania  
20.  033.87  65  Fujiwara Toneri  1  6  S  Japan  
21.  032.80  62  Arcy Leann  0  15  S  Philippines  
22.  032.03  52  Law Tik Shun  0  0  MT  Hong Kong  
23.  029.98  48  Nixon Balandra  2  46  MT  Philippines  
24.  029.67  54  Randy Orton  6  0  United States of America  
25.  029.46  60  Rindell Mabunga  1  31  S  Philippines  
26.  027.78  35  Arjun Singh Rajawat  0  4  ❂  S  India 
27.  026.68  41  Jacob Sabido  0  5  S  Philippines  
28.  023.82  41  Darwin Ojera  0  22  MT  Philippines  
29.  021.87  41  Joselito Torculas  3  26  Philippines  
30.  021.14  57  Roenz Joshlee Timbol  0  1  S  Philippines  
31.  020.99  36  Rik Smoody  0  0  MT  United States of America  
32.  020.99  36  Lim Jing Ren  0  0  S  Malaysia  
33.  020.63  26  Alea Astrea  0  0  ❂  S  Philippines 
34.  020.41  30  echo gabata  0  0  Vietnam  
35.  018.79  41  Hanz U. Baga  0  71  S  Philippines  
36.  017.88  26  Kuba Helsztynski  0  0  MT  Poland  
37.  016.82  28  Raffy Salazar  0  0  S  Philippines  
38.  015.08  19  Lenard Guillermo  0  2  ❂  S  Philippines 
39.  014.43  20  Gluttony  0  0  Philippines  
40.  014.29  18  Angelo M. Velasquez  0  5  ❂  S  Philippines 
41.  013.91  29  Joseph Rodelas  1  0  S  Philippines  
42.  013.23  20  Mark Alvero  0  0  MT  Philippines  
43.  013.09  26  Norwyn Nicholson Kah  0  38  S  Philippines  
44.  013.05  25  Jhepoy Dizon  0  0  S  Philippines  
45.  012.31  32  Daniel James Molina  0  1  S  Philippines  
46.  011.76  20  Ralph Macarasig  0  0  S  Philippines  
47.  011.18  26  Joem Canciller  0  0  Philippines  
48.  011.18  18  Maureen Jordan  0  1  Singapore  
49.  011.11  14  John Albert A. Reyes  0  6  ❂  S  Philippines 
50.  010.43  17  Nheil Ignacio  0  8  S  Philippines  
51.  010.11  22  Hanelet Santos  0  15  S  Philippines  
52.  010.00  23  Kumar Ayush  0  1  S  India  
53.  009.57  28  Mark Kenneth Dairo  0  26  S  Philippines  
54.  009.56  17  Ibrahim Demir  0  1  MT  Turkey  
55.  009.18  18  Francis Gerard Magtibay  0  0  S  Philippines  
56.  009.17  17  angelo magdaong  0  0  MT  Philippines  
57.  009.15  22  Christian Paul Patawaran  0  1  S  Philippines  
58.  009.07  20  Charles Dwight M. Pelaez  0  8  S  Philippines  
59.  008.95  19  Bikram Chohan  0  5  S  India  
60.  008.73  11  Melga Sonio  0  0  ❂  S  Philippines 
61.  008.38  13  Poetri Sonya Tarabunga  0  0  S  Indonesia  
62.  007.78  14  Ewen Goisot  0  17  France  
63.  007.39  11  Max Wong  0  0  S  Hong Kong  
64.  007.34  43  Kimi No Nawa  3  166  S  Japan  
65.  007.29  21  Christian Daang  1  25  S  Philippines  
66.  007.07  14  Angelu G. Leynes  1  0  S  Philippines  
67.  006.86  11  Mark Elis Espiridion  0  0  Philippines  
68.  006.55  17  Stefano Ongari  0  0  S  Italy  
69.  006.10  13  Chris Norman Algo  0  10  S  Philippines  
70.  005.56  7  Adrian Pilotos Burgos  0  0  ❂  Philippines  
71.  004.76  6  Yavuz Selim Koseoglu  2  0  ❂  S  Turkey 
72.  004.76  6  Mahmut Cemrek  0  0  ❂  Turkey  
73.  004.76  6  John Gamal Aziz Attia  2  1  ❂  S  Egypt 
74.  004.76  6  Jade N. Mijares  0  0  ❂  S  Philippines 
75.  003.83  13  Aljun Emperado  0  3  S  Philippines  
76.  003.40  27  Keedgwh  0  0  India  
77.  003.17  6  Kevin Durant  1  0  S  Turkey  
78.  003.17  6  John Lester Tan  0  0  S  Philippines  
79.  003.17  4  Βαρελάς Γεώρ𝛾ιος  0  0  ❂  Greece  
80.  002.83  5  Kot Behemot  0  0  MT  United States of America  
81.  002.38  3  Gerald M. Pascua  0  0  ❂  Philippines  
82.  001.98  5  Leandro Dar Juan  0  0  S  Philippines  
83.  001.81  4  Smahi Abdeslem  0  4  S  Algeria  
84.  001.59  6  David Paul  0  0  S  Philippines  
85.  001.59  2  James Harden  0  0  ❂  S  Philippines 
86.  001.43  3  John Kenneth Vito Cruz  0  0  S  Philippines  
87.  001.15  4  Mark David Mortel Dela Cruz  0  0  S  Philippines  
88.  001.06  2  Adnan Donmez  0  0  MT  Turkey  
89.  000.79  3  wow magic  0  0  S  Philippines  
90.  000.79  1  Suleyman Akarsu  0  0  ❂  Turkey  
91.  000.79  1  Serkan Callioglu  0  0  ❂  Turkey  
92.  000.79  1  Ryan Magdayo Caduyac  0  0  ❂  S  Philippines 
93.  000.79  1  Rosendo Parra Milian  0  1  ❂  S  Peru 
94.  000.79  1  Rafael Zamora  0  0  ❂  S  Philippines 
95.  000.79  1  Mohamed Karamany  1  0  ❂  Egypt  
96.  000.79  1  Evan Phillip Mendoza  0  0  ❂  S  Philippines 
97.  000.79  1  Captain Magneto  0  0  ❂  S  Germany 
98.  000.79  1  Adisa Tolani  0  0  ❂  S  Nigeria 
99.  000.45  2  Sam Kashkooli  0  0  S  Iran  
100.  000.40  1  Miguel  0  0  S  Philippines 
hide this All problems are solved 3178 times.
Score Table  Countries
NOTE: Countries are listed according to their first answer submit dates.
Country  # of Correct Answers  # of Trials  Performance 

Egypt  7  7  100% 
Philippines  2128  3099  68.67% 
Turkey  111  156  71.15% 
Greece  4  4  100% 
South Korea  63  74  85.14% 
Thailand  83  103  80.58% 
Indonesia  13  16  81.25% 
Japan  183  391  46.8% 
Malaysia  104  127  81.89% 
Peru  1  1  100% 
Algeria  4  7  57.14% 
India  143  338  42.31% 
Canada  117  128  91.41% 
Italy  17  35  48.57% 
Romania  51  60  85% 
United States of America  107  153  69.93% 
Germany  1  1  100% 
France  14  20  70% 
Poland  26  30  86.67% 
Hong Kong  64  81  79.01% 
Vietnam  30  35  85.71% 
Iran  2  8  25% 
Nigeria  1  1  100% 
China  118  134  88.06% 
Singapore  18  23  78.26% 
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Worked Solutions to the Problems
Solutions to all Challenging Math Problems are ready!
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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
I am not one of the most gifted math wizards from my country. Through AhMath, I am able to hone my skills and at least par with them, although I am still far from their prowess. Some simple questions are masked to seem difficult and all problems that I have solved felt satisfying knowing that I was able to use, display, and hone my skills.
 Fujiwara Toneri / Japan
This is a good website for math enthusiast who wants to challenge their math ability. Thanks for questions that push us to think differently and of course to learn new things.. More powers and God Bless.
 Reygan Dionisio / Philippines