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AhMath Real than i, rational than π

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A new problem will be published as soon as the latest problem gets at least 5 solvers. 1 more solver is needed to release the new problem.

☆★☆★☆★  Newest Problem!  ★☆★☆★☆

98. Problem: 93C4 , proposed by Ahmet Arduc
98 is the smallest number with the property that its first 5 multiples contain the digit 9.
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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.

Number of Responses: 2957
Number of Correct R.: 1960
Difficulty Level: 66.28
1. Problem: 595A , proposed by Ahmet Arduc, Tip: Key Fact(s): 7695
1 is the multiplicative identity.
Correct answers have been submitted by:
1. Mohamed Karamany
2. Jeffrey Robles
3. Joseph Rodelas
4. Mahmut Cemrek
5. Suleyman Akarsu
6. Yavuz Selim Koseoglu
7. John Gamal Aziz Attia
8. Serkan Callioglu
9. Βαρελάς Γεώρ𝛾ιος
10. Marvin Cato
11. Isaiah James de Dios Maling
12. Joselito Torculas
13. John Albert A. Reyes
14. Nheil Ignacio
15. Gerald M. Pascua
16. Angelu G. Leynes
17. Roenz Joshlee Timbol
18. Rindell Mabunga
19. Caed Mark Medul Mendoza
20. Russel J. Galanido
21. Melga Sonio
22. Mark Elis Espiridion
23. Adrian Pilotos Burgos
24. Sumet Ketsri
25. Daniel James Molina
26. Nixon Balandra
27. Jacob Sabido
28. Poetri Sonya Tarabunga
29. John Patrick
30. Lilanie Monique Torilla
31. Chris Norman Algo
32. Christian Daang
33. Grant Lewis Bulaong
34. Richard Phillip Dimaala Fernandez
35. Jake Gacuan
36. Ibrahim Demir
37. Christian Paul Patawaran
38. Amirul Faiz Abdul Muthalib
39. Norwyn Nicholson Kah
40. Jhepoy Dizon
41. Ralph Macarasig
42. Dan Lang
43. Chayapol
44. Dreimuru Tempest
45. Kurara Chibana
46. Lim Jing Ren
47. Alea Astrea
48. Kumar Ayush
49. Joem Canciller
50. Gluttony
51. Serdal Aslantas
52. Radu Bogo
53. Barry Villanueva
54. Randy Orton
55. Captain Magneto
56. Willie Revillame Wowowin
57. Mertkan Simsek
58. Mark Lawrence P Velasco
59. Srinivas Kanigiri
60. Prince Ivan Paraiso
61. Dale Angelo Azas Cortez
62. Mythreya Lakshman
63. Bikram Chohan
64. Law Tik Shun

Score Table - Math Enthusiasts

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.

Order Score # of Correct Answers Names Badges Country
94Caed Mark Medul Mendoza6109MT PhilippinesPhilippines
77Amirul Faiz Abdul Muthalib110MT MalaysiaMalaysia
67Lilanie Monique Torilla055S PhilippinesPhilippines
73Jeffrey Robles154 PhilippinesPhilippines
65Isaiah James de Dios Maling427 PhilippinesPhilippines
57Sumet Ketsri558 ThailandThailand
62Kurara Chibana40S JapanJapan
54Willie Revillame Wowowin00 PhilippinesPhilippines
63Russel J. Galanido130S South KoreaSouth Korea
61Richard Phillip Dimaala Fernandez464MT PhilippinesPhilippines
63Mertkan Simsek80MT TurkeyTurkey
50Marvin Cato130MT PhilippinesPhilippines
48Nixon Balandra346MT PhilippinesPhilippines
54Randy Orton60 United States of AmericaUnited States of America
60Rindell Mabunga131S PhilippinesPhilippines
34Arjun Singh Rajawat04S IndiaIndia
41Jacob Sabido05S PhilippinesPhilippines
41Joselito Torculas426 PhilippinesPhilippines
30Radu Bogo032 RomaniaRomania
36Lim Jing Ren00S MalaysiaMalaysia
26Alea Astrea00S PhilippinesPhilippines
32Law Tik Shun00MT Hong KongHong Kong
26Kuba Helsztynski00MT PolandPoland
19Lenard Guillermo02S PhilippinesPhilippines
20Gluttony00 PhilippinesPhilippines
40Roenz Joshlee Timbol01S PhilippinesPhilippines
26Norwyn Nicholson Kah038S PhilippinesPhilippines
25Jhepoy Dizon00S PhilippinesPhilippines
19Mark Alvero00MT PhilippinesPhilippines
32Daniel James Molina01S PhilippinesPhilippines
20Ralph Macarasig00S PhilippinesPhilippines
26Joem Canciller10 PhilippinesPhilippines
14John Albert A. Reyes06S PhilippinesPhilippines
17Nheil Ignacio08S PhilippinesPhilippines
23Kumar Ayush01S IndiaIndia
17Ibrahim Demir01MT TurkeyTurkey
22Christian Paul Patawaran01S PhilippinesPhilippines
19Bikram Chohan05S IndiaIndia
15Srinivas Kanigiri00S IndiaIndia
11Melga Sonio00S PhilippinesPhilippines
13Poetri Sonya Tarabunga00S IndonesiaIndonesia
12Andrew Chiu00 PhilippinesPhilippines
10Monu Baba Rura Sirsa Up00S IndiaIndia
14Ewen Goisot017 FranceFrance
43Kimi No Nawa8166S JapanJapan
21Christian Daang125S PhilippinesPhilippines
18James Ericson10 ThailandThailand
14Angelu G. Leynes10S PhilippinesPhilippines
11Mark Elis Espiridion00 PhilippinesPhilippines
17Stefano Ongari00S ItalyItaly
8Joseph Rodelas10S PhilippinesPhilippines
13Chris Norman Algo010S PhilippinesPhilippines
12Reymark Togno00 PhilippinesPhilippines
12Dreimuru Tempest20S PhilippinesPhilippines
7Adrian Pilotos Burgos00 PhilippinesPhilippines
10Mythreya Lakshman03 IndiaIndia
6Yavuz Selim Koseoglu20S TurkeyTurkey
6Mahmut Cemrek00 TurkeyTurkey
6John Gamal Aziz Attia21S EgyptEgypt
10Ikemen30 JapanJapan
7Emmanuel David00S PhilippinesPhilippines
27Keedgwh00 IndiaIndia
5Sigmund Dela Cruz05S PhilippinesPhilippines
4Chayapol02S ThailandThailand
5John Lester Tan00S PhilippinesPhilippines
5Hanelet Santos00S PhilippinesPhilippines
5Grant Lewis Bulaong01S PhilippinesPhilippines
3Gerald M. Pascua00 PhilippinesPhilippines
3Barry Villanueva02 PhilippinesPhilippines
5Jake Gacuan09 PhilippinesPhilippines
4Mark Lawrence P Velasco00S PhilippinesPhilippines
6Fred Gutierrez00S PhilippinesPhilippines
4Smahi Abdeslem04S AlgeriaAlgeria
5Dan Lang00 PhilippinesPhilippines
2Nathanael Joshua Balete00 PhilippinesPhilippines
2Edge Ramos00S PhilippinesPhilippines
2Afshiram Muhammed00S TurkeyTurkey
5John Marco Latagan00S PhilippinesPhilippines
2Judy Ann Rubante00S PhilippinesPhilippines
4Gerlie Emata Mantua01S PhilippinesPhilippines
2Evan Gruda00S United States of AmericaUnited States of America
1Suleyman Akarsu00 TurkeyTurkey
1Serkan Callioglu00 TurkeyTurkey
1Rosendo Parra Milian01S PeruPeru
1Rdvnaksu11S TurkeyTurkey
1Muhammed Aydogdu00 TurkeyTurkey
1Mohamed Karamany10 EgyptEgypt
1Kwok Ho Yin, Jaffy01S Hong KongHong Kong
1Captain Magneto00S GermanyGermany
1Avrila Frazier01MT United States of AmericaUnited States of America
1Abhishek Singh00S IndiaIndia
2Serdal Aslantas01MT RomaniaRomania
2John Rocel Perez00S PhilippinesPhilippines
1Prince Ivan Paraiso00S PhilippinesPhilippines
1Dale Angelo Azas Cortez01S PhilippinesPhilippines
2Melek Cimen11S TurkeyTurkey
1Ryan Quimo00S PhilippinesPhilippines
1Mark Allen Facun00S PhilippinesPhilippines
1John Patrick03S PhilippinesPhilippines
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  • Worked Solutions to the Problems
    Solutions to all Challenging Math Problems are ready!
    Solutions for the first 10 Challenging Math Problems
    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.

  • Books, Websites, etc.
    ✔   Singapore Mathematical Olympiads, from 2005 to 2013
    ✔   Solving Equations in Integers by A. O. Gelfond (1981)
    ✔   Solving Mathematical Problems - A Personal Perspective by Terence Tao (2006)
    ✔   Street-Fighting Mathematics - The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan (2010)
    ✔   Techniques of Problem Solving by Luis Fernandez, Steven G. Krantz (1997) (Solutions Manual)
    ✔   Techniques of Problem Solving by Steven G. Krantz (1997)
    ✔   The Art and Craft of Problem Solving, 2nd Ed. by Paul Zeitz (2007) instructor's manual.
    ✔   The Art and Craft of Problem Solving, 2nd Ed. by Paul Zeitz (2007)
    ✔   The Art of Mathematics - Coffee Time in Memphis by Béla Bollob?s (2006)
    ✔   The Art of Problem Posing, 3rd Ed. by Stephen I. Brown, Marion I. Walter (2005)
    ✔   The Art of Problem Solving - A Resource for the Mathematics Teacher by Alfred S. Posamentier, Wolfgang Schulz (1996)
    ✔   The Art of Problem Solving, Vol. 1 - The Basics by Sandor Lehoczky, Richard Rusczyk (2006)
    ✔   The Best Problems From Around the World by Cao Minh Quang (2006)
    ✔   The Canadian Mathematical Olympiad [1969-1993] by Michael Doob (1993)
    ✔   The Cauchy-Schwarz Master Class - An Introduction to the Art of Mathematical Inequalities (2004)
    ✔   The Colorado Mathematical Olympiad and Further Explorations From the Mountains of Colorado to the Peaks of Mathematics (2011)
    ✔   The Colossal Book of Mathematics - Classic Puzzles, Paradoxes, and Problems by Martin Gardner (2001)
    ✔   The Geometry of Numbers by C. D. Olds, Anneli Lax (2000)
    ✔   The Green Book of Mathematical Problems by Kenneth Hardy, Kenneth S. Williams (1985)
    ✔   The Higher Arithmetic - An Introduction to the Theory of Numbers, 8th Ed. by H. Davenport (2008)
    ✔   The IMO Compendium - A Collection of Problems Suggested for the International Mathematical Olympiads [1959-2009] 2nd Ed. (2011)
    ✔   The Last Recreations - Hydras, Eggs, and Other Mathematical Mystifications by Martin Gardner (1997)
    ✔   The Magic Numbers of Dr. Matrix by Martin Gardner (1985)
    ✔   The Math Problems Notebook by Valentin Boju, Louis Funar (2007)
    ✔   The Mathemagician and Pied Puzzler - A Collection in Tribute to Martin Gardner by Elwyn R. Berlekamp, Tom Rodgers (1999)
    ✔   The Mathematical Recreations of Lewis Carroll - Pillow Problems and a Tangled Tale (1958)
    ✔   The Mathematics of Ciphers - Number Theory and RSA Cryptography by S.C. Coutinho (1999)
    ✔   The Mathscope - All the Best From Vietnamese Problem Solving Journals (2007)
    ✔   The Method of Mathematical Induction by I. S. Sominskii (1961)
    ✔   The Moscow Puzzles - 359 Mathematical Recreations by Boris A. Kordemsky (1972)
    ✔   The New Mathlete Problem Book with Sample Solutions and Appendices (1977)
    ✔   The New York City Contest Problem Book - Problems and Solutions from the New York City Interscholastic Mathematics..(1986)
    ✔   The Penguin Book of Curious and Interesting Geometry by David Wells (1991)
    ✔   The Penguin Book of Curious and Interesting Numbers by David Wells (1986)
    ✔   The Penguin Book of Curious and Interesting Puzzles by David Wells (1992)
    ✔   The Pleasures of Pi,e and Other Interesting Numbers by Y. E. O. Adrian (2006)
    ✔   The Quest for Functions - Functional Equations for the Beginners by Paul Vaderlind (2005)
    ✔   The Red Book of Mathematical Problems by Kenneth S. Williams, Kenneth Hardy (1988)
    ✔   The Square Root of 2 - A Dialogue Concerning a Number and a Sequence by David Flannery (2006)
    ✔   The Stanford Mathematics Problem Book - With Hints and Solutions by George Polya, Jeremy Kilpatrick (1974)
    ✔   The Theory of Numbers - A Text and Source Book of Problems by Andrew Adler, John E. Cloury (1995)
    ✔   The Unexpected Hanging and Other Mathematical Diversions by Martin Gardner (1991)
    ✔   The Universe in a Handkerchief - Lewis Carroll’s Mathematical Recreations, Games, Puzzles, and Word Plays (1996)
    ✔   The USSR Olympiad Problem Book - Selected Problems and Theorems of Elementary Mathematics (1993)
    ✔   The William Lowell Putnam Mathematical Competition - Problems and Solutions [1938-1964] (1980)
    ✔   The William Lowell Putnam Mathematical Competition - Problems and Solutions [1965–1984] (1985)
    ✔   The William Lowell Putnam Mathematical Competition - Problems, Solutions, and Commentary [1985-2000] (2002)
    ✔   The William Lowell Putnam Mathematical Competition - Problems, Solutions, and Commentary [2001-2008] (2008)
    ✔   The Wohascum County Problem Book by George T. Gilbert (1993)
    ✔   The Wonders of Magic Squares by Jim Moran (1982)
    ✔   Time Travel and Other Mathematical Bewilderments by Gardner Martin (1988)
    ✔   Topics in Algebra and Analysis - Preparing for the Mathematical Olympiad by Radmila Bulajich Manfrino (2015)
    ✔   Trigonometric Delights by Eli Maor (1998)
    ✔   USA and International Mathematical Olympiads [2004] by Titu Andreescu, Zuming Feng (2005)
    ✔   USA and International Mathematical Olympiads [2006-2007] by Zuming Feng, Yufei Zhao
    ✔   USA Mathematical Olympiads [1972-1986] Compiled and with Solutions by Murray S. Klamkin (1988)
    ✔   Variance on Topics of Plane Geometry by Florentin Smarandache (2013)
    ✔   What Is the Name of This Book - The Riddle of Dracula and Other Logical Puzzles by Raymond M. Smullyan (1978)
    ✔   What to Solve - Problems and Suggestions for Young Mathematicians by Judita Cofman (1990)
    ✔   Wheels, Life and Other Mathematical Amusements by Martin Gardner (1983)
    ✔   When Less is More - Visualizing Basic Inequalities by Claudi Alsina, Roger Nelsen (2009)
    ✔   Which Way Did the Bicycle Go by Konhauser, Velleman, Wagon (1996)
    ✔   Winning Solutions by Edward Lozansky, Cecil Rousseau (1996)
  • Key Facts
    Key Fact 7446 |Tags: product,rational,number,irrational
    Key Fact 7695 |Tags: fraction,lowest term,numerator,denominator,relatively prime
    Key Fact ABAD |Tags: square,even,integer,divisibility
    Key Fact BAB3 |Tags: square,odd,integer,divisibility
    Key Fact 988C |Tags: product,perfect square,consecutive numbers
    Key Fact 9A34 |Tags: divisibility
    Key Fact B664 |Tags: identity,factorial
    Key Fact 969B |Tags: identity
    Key Fact CE81 |Tags: identity
    Key Fact B945 |Tags: identity
    Key Fact BCC8 |Tags: factorial,inequality
    Key Fact 965A |Tags: identity
    Key Fact E856 |Tags: identity
    Key Fact 7C45 |Tags: Sophie-Germain,identity
    Key Fact EA1C |Tags: identity
    Key Fact 3E17 |Tags: identity,factorization
    Key Fact 2545 |Tags: identity,factorization
    Key Fact A376 |Tags: identity
    Key Fact 3278 |Tags: composite number
    Key Fact 2DCC |Tags: prime number,definition
    Key Fact 87D4 |Tags: prime number,composite number,1
    Key Fact 9E11 |Tags: prime number,composite number,1
    Key Fact A478 |Tags: prime number,even
    Key Fact 2AB2 |Tags: prime number
    Key Fact DAEA |Tags: prime numbers
    Key Fact 9ECE |Tags: prime factorization
    Key Fact 525C |Tags: prime number,composite number
    Key Fact 163E |Tags: Wilson's Theorem
    Key Fact 5221 |Tags: Bertrand's Postulate,prime number
    Key Fact 24D6 |Tags: Bonse's Inequality,prime numbers
    Key Fact C181 |Tags: prime,divisor
    Key Fact 8A33 |Tags: divisibility,square,odd,integer
    Key Fact 7B55 |Tags: divisibility
    Key Fact 8C41 |Tags: divisibility
    Key Fact 8632 |Tags: product,consecutive,integer,divisibility
    Key Fact EADA |Tags: divisibility
    Key Fact A4A7 |Tags: binomial expansion
    Key Fact 3845 |Tags: binomial expansion,number of terms
    Key Fact D8CD |Tags: identity
    Key Fact DEA5 |Tags: identity
    Key Fact 7B38 |Tags: identity
    Key Fact 2EBB |Tags: identity
    Key Fact 89DD |Tags: identity
    Key Fact ECD9 |Tags: chessboard,square
    Key Fact A86B |Tags: arithmetic mean,real numbers
    Key Fact B65C |Tags: geometric mean,real numbers
    Key Fact D477 |Tags: arithmetic mean,geometric mean,inequality
    Key Fact DDC5 |Tags: harmonic mean,real numbers
    Key Fact 29D9 |Tags: arithmetic mean,harmonic mean,inequality
    Key Fact 5375 |Tags: inequality
    Key Fact 1E7C |Tags: inequality
    Key Fact 3981 |Tags: inequality
    Key Fact 1EB9 |Tags: inequality,identity
    Key Fact D7B8 |Tags: inequality
    Key Fact 2483 |Tags: inequality
    Key Fact 6C13 |Tags: inequality
    Key Fact 7185 |Tags: inequality
    Key Fact 8C62 |Tags: inequality
    Key Fact 913D |Tags: inequality,identity
    Key Fact ADBA |Tags: Cauchy–Schwarz,inequality
    Key Fact 2169 |Tags: Chebyshev,inequality
    Key Fact E1B9 |Tags: line,intersection,parabola,abscissa,vertex,midpoint,line segment
    Key Fact 72A4 |Tags: De Moivre,formula
    Key Fact 5DB3 |Tags: fibonacci,numbers
    Key Fact 47EB |Tags: finite serie,finite sequence
    Key Fact 13D3 |Tags: infinite serie,infinite sequence
    Key Fact EAA4 |Tags: partial sum,series
    Key Fact 3332 |Tags: sequence,partial sum,series,limit
    Key Fact 2B69 |Tags: sequence,partial sum,series,limit
    Key Fact C62B |Tags: series,sum
    Key Fact 1529 |Tags: sum,infinite serie
    Key Fact E6E7 |Tags: relative error,measurement
    Key Fact 8B56 |Tags: angle,bisector,triangle
    Key Fact B4C3 |Tags: sum,exterior angles,convex,polygon
    Key Fact C4CC |Tags: triangle,circle,greatest area,isosceles triangle
    Key Fact 8146 |Tags: circle,plane,common tangent
    Key Fact B13A |Tags: lattice points,gcd,greatest common divisor
    Key Fact 4BC8 |Tags: right triangle,median

If you want to be a contractor (problem writer, key fact writer, etc.), please contact AhMath by sending an email to challenging-problems@ahmath.com.

Amirul Faiz Abdul Muthalib

Amirul Faiz Abdul Muthalib

Problem Writer

Number of problems: 10

With over 5 years of hands-on, successful teaching experience, Amirul is an enthusiastic Pre-University 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

İhsan Yücel

Problem Writer

Number of problems: 3

I am currently in the thesis phase of my postgraduate education which is about mathematics teaching education. I got some notable national and international achievements in various secondary school mathematics national and international project competitions. Likewise, my students also got many elementary and secondary level mathematical olympics achievements. In the recent past, my students got the first and the second place in the TÜBİTAK National Secondary School Research Projects Contest. One of my students, Read More a team member of the national math team, received a bronze medal in IMO. I'm an author of many scientific articles about mathematics in the quarterly magazine "Mathematical World". I'm the founder of Matematik Meraklısı, which is a website dedicated to Mathematics. Read Less

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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 non-mathematical 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 self-paced 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 non-students to further enhance their math skills. God bless and More power AHMATH FTW!!!

- Isaiah James de Dios Maling / Philippines

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