A new problem will be released soon.
Arf League
 Who is Cahit Arf? What is Arf League?

Info and Announcements
Info
✔ There are 132 problems and 82 key facts, waiting for math enthusiasts! Dear Math Enthusiasts,
Thanks for your interest in Arf League.
✔ Among 1.12 billion active websites, AhMath is now within the top 0.014862%, and we hope its position will get better soon. We try to serve the best for all of you.
✔ Please feel free to send your comments and suggestions to challengingproblems@ahmath.com and help us to promote this lovely activity by distributing the
Arf League Poster and the QR Code.
✔ Arf League is looking for new problem and/or key fact writers. If you are interested in writing challenging math problems and/or key facts, please contact us. We'll be glad to meet with new question writers.
hide this To submit your answers you need to log in.
If you are not a member of this page and if your name is not listed in the score tables, you need to sign up first. Otherwise, please read the following instructions given below!
hide this This is the place where you can find the most valuable Mathematical Olympiads books!
New pages from AhMath: Unordered Times Table, Unordered Divisibility Test, Bulls and Cows Game, Unique Bid Auction Game, and Guess My Country. Check them out!
Explore all your possibilities. Udemy online courses on sale from $11.99 New Problem
 Previous Problems
 Score Tables
 Books, Key Facts, etc.
 HQTs
 Testimonials
 Donate / Become a Patron
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
7611
by Hanlee Wong
Long Jumper
Marathon Runner
since 11.11.2019
78937
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!
Joem Cancillercharles edward
Jay Lee
Romeo Dane D. Melendrez
Order  Score  # of Correct Answers  Names  Badges  Country  

FS  SF  SP  UT  
1.  097.73  130  Angelo M. Velasquez  130  47  S  Philippines  
2.  083.69  127  Lee Csek  127  2  China  
3.  083.63  117  Lisa Sauermann  117  2  S  Germany  
4.  083.05  123  Zhuo Qun Song  123  2  S  Canada  
5.  076.71  122  Daryll Ko  122  0  S  Philippines  
6.  076.48  115  Isaiah James de Dios Maling  115  34  MT  Philippines  
7.  075.22  128  Caed Mark Medul Mendoza  128  112  MT  Philippines  
8.  060.31  94  Jeffrey Robles  94  5  Philippines  
9.  056.20  103  Reygan Medina Dionisio  103  2  MT  Philippines  
10.  052.13  92  Richard Phillip Dimaala Fernandez  92  90  MT  Philippines  
11.  050.76  67  Lilanie Monique Torilla  67  55  ❂  S  Philippines 
12.  049.96  84  Jereco Dela Pena  84  0  MT  Philippines  
13.  047.77  65  Sumet Ketsri  65  67  Thailand  
14.  045.46  71  Amirul Faiz Abdul Muthalib  71  0  MT  Malaysia  
15.  042.43  69  Radu Bogo  69  45  Romania  
16.  041.86  59  Hanlee Wong  59  63  S  Singapore  
17.  041.02  62  Kurara Chibana  62  0  S  Japan  
18.  040.91  54  Willie Revillame Wowowin  54  0  ❂  Philippines  
19.  040.63  63  Russel J. Galanido  63  30  S  South Korea  
20.  035.87  66  Mertkan Simsek  66  0  MT  Turkey  
21.  035.82  79  Christian Paul C. Patawaran  79  1  S  Philippines  
22.  035.06  54  Marvin Cato  51  30  MT  Philippines  
23.  031.73  66  Fujiwara Toneri  66  6  S  Japan  
24.  031.31  62  Arcy Leann  62  15  S  Philippines  
25.  030.57  52  Law Tik Shun  52  0  MT  Hong Kong  
26.  028.61  48  Nixon Balandra  48  46  MT  Philippines  
27.  028.32  54  Randy Orton  54  0  United States of America  
28.  028.12  60  Rindell Mabunga  60  31  S  Philippines  
29.  027.15  49  Raffy Salazar  49  0  S  Philippines  
30.  026.52  35  Arjun Singh Rajawat  35  4  ❂  S  India 
31.  025.57  45  Rik Smoody  45  0  MT  United States of America  
32.  025.47  41  Jacob Sabido  41  5  S  Philippines  
33.  022.74  41  Darwin Ojera  41  22  MT  Philippines  
34.  020.88  41  Joselito Torculas  41  26  Philippines  
35.  020.18  57  Roenz Joshlee Timbol  57  1  S  Philippines  
36.  020.04  36  Lim Jing Ren  36  0  S  Malaysia  
37.  019.70  26  Alea Astrea  26  0  ❂  S  Philippines 
38.  019.48  30  echo gabata  30  0  Vietnam  
39.  019.25  36  Lourenz Miguel Paras  36  0  S  Philippines  
40.  017.44  41  Hanz U. Baga  41  73  S  Philippines  
41.  017.07  26  Kuba Helsztynski  26  0  MT  Poland  
42.  015.06  26  Sajib Kumar Chowdhury  26  0  S  Bangladesh  
43.  014.39  19  Lenard Guillermo  19  2  ❂  S  Philippines 
44.  013.77  20  Gluttony  20  0  Philippines  
45.  013.64  30  Angelo Bungcaras Magdaong  30  1  MT  Philippines  
46.  013.27  29  Joseph Rodelas  29  0  S  Philippines  
47.  012.63  20  Mark Alvero  20  0  MT  Philippines  
48.  012.49  26  Norwyn Nicholson Kah  26  38  S  Philippines  
49.  012.46  25  Jhepoy Dizon  25  0  S  Philippines  
50.  012.43  19  Ramon Villota  19  0  S  Philippines  
51.  011.75  32  Daniel James Molina  32  1  S  Philippines  
52.  011.22  20  Ralph Macarasig  20  0  S  Philippines  
53.  011.16  18  Ric Tura Jr  18  21  S  Philippines  
54.  010.67  18  Maureen Jordan  18  1  Singapore  
55.  010.61  14  John Albert A. Reyes  14  6  ❂  S  Philippines 
56.  009.95  17  Nheil Ignacio  17  8  S  Philippines  
57.  009.65  22  Hanelet Santos  22  15  S  Philippines  
58.  009.54  23  Kumar Ayush  23  1  S  India  
59.  009.14  28  Mark Kenneth Dairo  28  26  S  Philippines  
60.  009.12  17  Ibrahim Demir  17  1  MT  Turkey  
61.  008.77  18  Francis Gerard Magtibay  18  0  S  Philippines  
62.  008.66  20  Charles Dwight M. Pelaez  20  8  S  Philippines  
63.  008.55  19  Bikram Chohan  19  5  S  India  
64.  008.33  11  Melga Sonio  11  0  ❂  S  Philippines 
65.  008.29  19  angelo magdaong  19  0  MT  Philippines  
66.  008.00  13  Poetri Sonya Tarabunga  13  0  S  Indonesia  
67.  007.42  14  Ewen Goisot  14  17  France  
68.  007.05  11  Max Wong  11  0  S  Hong Kong  
69.  007.00  43  Kimi No Nawa  43  166  S  Japan  
70.  006.96  21  Christian Daang  21  25  S  Philippines  
71.  006.75  14  Angelu G. Leynes  14  0  S  Philippines  
72.  006.55  11  Mark Elis Espiridion  11  0  Philippines  
73.  006.26  17  Stefano Ongari  17  0  S  Italy  
74.  005.82  13  Chris Norman Algo  13  10  S  Philippines  
75.  005.30  7  Adrian Pilotos Burgos  7  0  ❂  Philippines  
76.  004.55  6  Yavuz Selim Koseoglu  6  0  ❂  S  Turkey 
77.  004.55  6  Mahmut Cemrek  6  0  ❂  Turkey  
78.  004.55  6  John Gamal Aziz Attia  6  1  ❂  S  Egypt 
79.  004.55  6  Jade N. Mijares  6  0  ❂  S  Philippines 
80.  003.66  13  Aljun Emperado  13  3  S  Philippines  
81.  003.25  27  Keedgwh  27  0  India  
82.  003.03  6  Liu Chen  6  0  China  
83.  003.03  6  Kevin Durant  6  0  S  Turkey  
84.  003.03  6  John Lester Tan  6  0  S  Philippines  
85.  003.03  4  Vaibhav Priyadarshi  4  0  ❂  S  India 
86.  003.03  4  Βαρελάς Γεώρ𝛾ιος  4  0  ❂  Greece  
87.  002.71  5  Kot Behemot  5  0  MT  United States of America  
88.  002.42  4  Saket Singh Rajawat  4  1  S  India  
89.  002.42  4  Bryant Ularte  4  0  MT  Philippines  
90.  002.27  3  Jomari Mama  3  0  ❂  MT  Philippines 
91.  002.27  3  Gerald M. Pascua  3  0  ❂  Philippines  
92.  001.89  5  Leandro Dar Juan  5  0  S  Philippines  
93.  001.89  5  Ian Galang  5  0  S  Philippines  
94.  001.73  4  Smahi Abdeslem  4  4  S  Algeria  
95.  001.73  4  Elijah Evangelista  4  0  S  Palau  
96.  001.52  6  David Paul  6  0  S  Philippines  
97.  001.52  4  Luke Robitaille  3  1  S  United States of America  
98.  001.52  2  James Harden  2  0  ❂  S  Philippines 
99.  001.36  3  John Kenneth Vito Cruz  3  0  S  Philippines  
100.  001.10  4  Mark David Mortel Dela Cruz  4  0  S  Philippines 
hide this All problems are solved 3699 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  2459  3540  69.46% 
Turkey  111  156  71.15% 
Greece  4  4  100% 
South Korea  63  74  85.14% 
Thailand  87  107  81.31% 
Indonesia  13  16  81.25% 
Japan  184  396  46.46% 
Malaysia  107  133  80.45% 
Peru  1  1  100% 
Algeria  4  7  57.14% 
India  151  340  44.41% 
Canada  127  145  87.59% 
Italy  17  35  48.57% 
Romania  71  90  78.89% 
United States of America  117  167  70.06% 
Germany  118  125  94.4% 
France  14  20  70% 
Poland  26  30  86.67% 
Hong Kong  64  82  78.05% 
Vietnam  30  35  85.71% 
Iran  2  8  25% 
Nigeria  1  1  100% 
China  133  155  85.81% 
Singapore  77  86  89.53% 
Bangladesh  26  34  76.47% 
Palau  4  7  57.14% 
Argentina  0  2  0% 

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.

Online Problem Solver
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 problem (or key fact) writer, please contact AhMath by sending an email to challengingproblems@ahmath.com.
Ahmet Arduc
Question Writer
Number of questions: 113Ahmet worked as a maths olympiad instructor for many years. He is the editor and coauthor of the unpublished 484page book “Mathematical Olympiad Preliminary Question Bank, with 1001 solved questions”. His students got high achievements in many local and national mathematical competitions.
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 Master’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.
İhsan Yücel
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. He’s an author of many scientific articles about mathematics in the quarterly magazine "Mathematical World". He’s the founder of Matematik Meraklısı, 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).
You?
Subject?
Leave a Comment!
Please use the form below to send your general comments about Arf League. All fields are required!
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
Most Active Modules
Explore all your possibilities. Udemy online courses on sale from $11.99 Go to top of page