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Format of the tags: Problem Code (Difficulty Level). All problems are solved 1569 times.
595A (0.77)
B28E (0.92)
A275 (0.83)
2BE2 (0.66)
218D (0.88)
A13E (0.39)
52D2 (0.92)
79B2 (0.69)
11C8 (0.76)
AC82 (0.62)
C1B5 (0.85)
24B8 (0.82)
6392 (0.98)
615D (0.81)
A836 (0.44)
7B83 (0.86)
E328 (0.63)
B613 (0.9)
EE2C (0.6)
E4C6 (1)
ABBA (0.22)
DAB1 (0.94)
D36C (0.67)
D7C4 (0.45)
A4C5 (0.81)
A378 (0.71)
3DC5 (0.68)
9E31 (0.4)
EEAA (0.81)
442B (0.57)
B854 (0.68)
95E3 (0.92)
3E1C (0.34)
1715 (0.5)
C877 (0.63)
C2BC (0.73)
E4AE (0.83)
57BD (0.88)
3785 (0.83)
2783 (0.66)
398B (0.86)
DE1D (0.87)
B87D (0.83)
C426 (0.59)
143B (0.85)
7964 (0.74)
76AC (0.88)
D256 (0.82)
8D49 (0.76)
7E39 (0.56)
4E84 (0.69)
EE37 (0.76)
2D73 (0.38)
E584 (0.3)
86C7 (0.71)
DAA3 (0.7)
7B63 (0.89)
5484 (0.67)
B18D (0.78)
B57E (1)
B375 (0.44)
A3BD (0.89)
513D (1)
D8E1 (0.63)
89E9 (0.67)
792C (0.83)
1D15 (0.07)
BB2C (0.25)
C294 (1)
D8E5 (0.8)
99E4 (0.33) (NEWEST PROBLEM) 
1. Problem: 595A , proposed by Ahmet Arduc, Tip: Key Fact(s): 7695
1 is the multiplicative identity.
$$\small{A=\frac{1}{1\times2\times3}+\frac{2}{3\times4\times5}+\frac{3}{5\times6\times7}+\cdots+\frac{2016}{4031\times4032\times4033}}$$If $A$ is written in its simplest form as $\frac{a}{b}$, what is $a+b$ $?$ Ah Math

  • 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
 
2. Problem: B28E , proposed by Ahmet Arduc
2 is the only even prime.
Find the smallest natural number $n$ such that the last five digits of the product of $\\$ $n$$\times$935$\times$972$\times$975 are all zero. Ah Math

  • Correct answers have been submitted by:
    1. Jeffrey Robles
    2. Joseph Rodelas
    3. Yavuz Selim Koseoglu
    4. John Gamal Aziz Attia
    5. Mahmut Cemrek
    6. Βαρελάς Γεώρ𝛾ιος
    7. Isaiah James de Dios Maling
    8. Adrian Pilotos Burgos
    9. Joselito Torculas
    10. Nheil Ignacio
    11. Jacob Sabido
    12. Gerald M. Pascua
    13. Russel J. Galanido
    14. John Albert A. Reyes
    15. Roenz Joshlee Timbol
    16. Marvin Cato
    17. Rindell Mabunga
    18. Chris Norman Algo
    19. Melga Sonio
    20. Mark Elis Espiridion
    21. Angelu G. Leynes
    22. Caed Mark Medul Mendoza
    23. Sumet Ketsri
    24. Richard Phillip Dimaala Fernandez
    25. Daniel James Molina
    26. Nixon Balandra
    27. Poetri Sonya Tarabunga
    28. Lilanie Monique Torilla
    29. Christian Daang
    30. Emmanuel David
    31. Christian Paul Patawaran
    32. Jake Gacuan
    33. Ibrahim Demir
    34. Amirul Faiz Abdul Muthalib
    35. Norwyn Nicholson Kah
    36. Joem Canciller
    37. Ralph Macarasig
    38. Jhepoy Dizon
    39. Lim Jing Ren
    40. John Marco Latagan
    41. Dan Lang
    42. Lenard Guillermo
    43. Hanelet Santos
    44. Dreimuru Tempest
    45. Dreimuru Tempest
    46. Srinivas Kanigiri
    47. Kurara Chibana
    48. Alea Astrea
    49. Kumar Ayush
    50. Reymark Togno
    51. Gluttony
    52. Mark Alvero
    53. Radu Bogo
    54. Stefano Ongari
    55. Randy Orton
    56. Willie Revillame Wowowin
    57. Mertkan Simsek
 
3. Problem: A275 , proposed by Ahmet Arduc, Tip: Key Fact(s): 7695
3 is the only prime 1 less than a perfect square.
$$A=\small{\frac{1}{2}+\frac{1}{2+4}+\frac{1}{2+4+6}+\cdots+\frac{1}{2+4+6+\cdots+4032}}$$If $A$ is written in its simplest form as $\frac{a}{b}$, what is $a+b$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Jeffrey Robles
    2. Muhammed Aydo?du
    3. Joseph Rodelas
    4. Mahmut Cemrek
    5. Yavuz Selim Koseoglu
    6. John Gamal Aziz Attia
    7. Isaiah James de Dios Maling
    8. John Albert A. Reyes
    9. Jacob Sabido
    10. Gerald M. Pascua
    11. Joselito Torculas
    12. Nheil Ignacio
    13. Russel J. Galanido
    14. Angelu G. Leynes
    15. Adrian Pilotos Burgos
    16. Roenz Joshlee Timbol
    17. Chris Norman Algo
    18. Rindell Mabunga
    19. Melga Sonio
    20. Mark Elis Espiridion
    21. Marvin Cato
    22. Richard Phillip Dimaala Fernandez
    23. Caed Mark Medul Mendoza
    24. Sumet Ketsri
    25. Nixon Balandra
    26. Daniel James Molina
    27. Poetri Sonya Tarabunga
    28. Lilanie Monique Torilla
    29. Christian Daang
    30. Christian Paul Patawaran
    31. Jake Gacuan
    32. Ibrahim Demir
    33. Amirul Faiz Abdul Muthalib
    34. Norwyn Nicholson Kah
    35. Joem Canciller
    36. Jhepoy Dizon
    37. Dan Lang
    38. Mark Alvero
    39. Chayapol
    40. Rosendo Parra Milian
    41. Dreimuru Tempest
    42. Srinivas Kanigiri
    43. Kurara Chibana
    44. Lim Jing Ren
    45. James Ericson
    46. Alea Astrea
    47. Kumar Ayush
    48. Gluttony
    49. Radu Bogo
    50. Stefano Ongari
    51. Barry Villanueva
    52. Reymark Togno
    53. Randy Orton
    54. Willie Revillame Wowowin
 
4. Problem: 2BE2 , proposed by Ahmet Arduc
4 is the smallest number of colors sufficient to color all planar maps.
What is the units digit of the sum $1^2+2^3+3^4+\cdots+2016^{2017}$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Angelu G. Leynes
    2. Jeffrey Robles
    3. Isaiah James de Dios Maling
    4. Joselito Torculas
    5. Russel J. Galanido
    6. Marvin Cato
    7. Rindell Mabunga
    8. John Albert A. Reyes
    9. Nheil Ignacio
    10. Caed Mark Medul Mendoza
    11. Sumet Ketsri
    12. Richard Phillip Dimaala Fernandez
    13. Daniel James Molina
    14. Nixon Balandra
    15. Lilanie Monique Torilla
    16. Mark Elis Espiridion
    17. Jacob Sabido
    18. Emmanuel David
    19. Jake Gacuan
    20. Christian Paul Patawaran
    21. Roenz Joshlee Timbol
    22. Ibrahim Demir
    23. Amirul Faiz Abdul Muthalib
    24. Norwyn Nicholson Kah
    25. John Lester Tan
    26. Ralph Macarasig
    27. Jhepoy Dizon
    28. Chayapol
    29. Dreimuru Tempest
    30. Kurara Chibana
    31. Lim Jing Ren
    32. James Ericson
    33. Alea Astrea
    34. Lenard Guillermo
    35. Radu Bogo
    36. Randy Orton
    37. Willie Revillame Wowowin
 
5. Problem: 218D , proposed by Ahmet Arduc
The sum of the first 73 odd primes is divisible by 73.
Find the remainder when $\underbrace{20172017\cdots2017}_{2017\text{ times}}$ is divided by 73. Ah Math

  • Correct answers have been submitted by:
    1. Yavuz Selim Koseoglu
    2. John Gamal Aziz Attia
    3. Mahmut Cemrek
    4. Joseph Rodelas
    5. Jeffrey Robles
    6. Isaiah James de Dios Maling
    7. Nheil Ignacio
    8. Roenz Joshlee Timbol
    9. Marvin Cato
    10. Russel J. Galanido
    11. Joselito Torculas
    12. Melga Sonio
    13. Angelu G. Leynes
    14. Caed Mark Medul Mendoza
    15. Sumet Ketsri
    16. John Albert A. Reyes
    17. Nixon Balandra
    18. Jacob Sabido
    19. Daniel James Molina
    20. Lilanie Monique Torilla
    21. Mark Elis Espiridion
    22. Poetri Sonya Tarabunga
    23. Richard Phillip Dimaala Fernandez
    24. Rindell Mabunga
    25. Jake Gacuan
    26. Grant Lewis Bulaong
    27. Christian Paul Patawaran
    28. Ibrahim Demir
    29. Amirul Faiz Abdul Muthalib
    30. Norwyn Nicholson Kah
    31. John Lester Tan
    32. Joem Canciller
    33. Jhepoy Dizon
    34. Lenard Guillermo
    35. Dan Lang
    36. Fred Gutierrez
    37. Mark Alvero
    38. Chayapol
    39. Kurara Chibana
    40. Alea Astrea
    41. Lim Jing Ren
    42. Gluttony
    43. Radu Bogo
    44. Stefano Ongari
    45. Randy Orton
    46. Willie Revillame Wowowin
 
6. Problem: A13E , proposed by Ahmet Arduc
2017 is a prime number.
If $a^2+b^2+c^2+d^2=2017$, what is the minimum value of $$\small{(a+b+c)^2+(b+c+d)^2+(c+d+a)^2+(d+a+b)^2\text{ ?}}$$ Ah Math

  • Correct answers have been submitted by:
    1. Jeffrey Robles
    2. Βαρελάς Γεώρ𝛾ιος
    3. Isaiah James de Dios Maling
    4. Joselito Torculas
    5. Marvin Cato
    6. Russel J. Galanido
    7. Melga Sonio
    8. Nheil Ignacio
    9. Sumet Ketsri
    10. Lilanie Monique Torilla
    11. Nixon Balandra
    12. Caed Mark Medul Mendoza
    13. Poetri Sonya Tarabunga
    14. Rindell Mabunga
    15. Richard Phillip Dimaala Fernandez
    16. Christian Paul Patawaran
    17. Amirul Faiz Abdul Muthalib
    18. Daniel James Molina
    19. Norwyn Nicholson Kah
    20. Jhepoy Dizon
    21. Lenard Guillermo
    22. Kurara Chibana
    23. Afshiram Muhammed
    24. Jacob Sabido
    25. Roenz Joshlee Timbol
 
7. Problem: 52D2 , proposed by Ahmet Arduc
7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass.
Find the value of $$\small{\frac{1}{2}+\frac{1}{3}+\frac{2}{3}+\frac{1}{4}+\frac{2}{4}+\frac{3}{4}+\frac{1}{5}+\cdots+\frac{2015}{2017}+\frac{2016}{2017}}$$ Ah Math

  • Correct answers have been submitted by:
    1. Melek Cimen
    2. Joseph Rodelas
    3. Yavuz Selim Koseoglu
    4. Mahmut Cemrek
    5. Jeffrey Robles
    6. Βαρελάς Γεώρ𝛾ιος
    7. Isaiah James de Dios Maling
    8. John Albert A. Reyes
    9. Nheil Ignacio
    10. Adrian Pilotos Burgos
    11. Joselito Torculas
    12. Rindell Mabunga
    13. Roenz Joshlee Timbol
    14. Marvin Cato
    15. Russel J. Galanido
    16. Angelu G. Leynes
    17. Melga Sonio
    18. Caed Mark Medul Mendoza
    19. Sumet Ketsri
    20. Daniel James Molina
    21. Nixon Balandra
    22. Lilanie Monique Torilla
    23. Mark Elis Espiridion
    24. Christian Daang
    25. Emmanuel David
    26. Jacob Sabido
    27. Poetri Sonya Tarabunga
    28. Richard Phillip Dimaala Fernandez
    29. Grant Lewis Bulaong
    30. Ibrahim Demir
    31. Amirul Faiz Abdul Muthalib
    32. Norwyn Nicholson Kah
    33. Christian Paul Patawaran
    34. Joem Canciller
    35. Ralph Macarasig
    36. Jhepoy Dizon
    37. Lim Jing Ren
    38. Lenard Guillermo
    39. Mark Alvero
    40. Dreimuru Tempest
    41. Kurara Chibana
    42. James Ericson
    43. Alea Astrea
    44. Reymark Togno
    45. Gluttony
    46. Radu Bogo
    47. Randy Orton
    48. Willie Revillame Wowowin
    49. Evan Gruda
 
8. Problem: 79B2 , proposed by Ahmet Arduc
8 is the largest cube in the Fibonacci sequence.
If $n$ is a positive even multiple of 5 and $$\small{8^2+10^2+12^2+18^2+20^2+22^2+\cdots+(n-2)^2+n^2+(n+2)^2}$$ is divisible by 9, what is the minumum value of $n$ $ ?$ Ah Math

  • Correct answers have been submitted by:
    1. Yavuz Selim Koseoglu
    2. Mahmut Cemrek
    3. Jeffrey Robles
    4. Nheil Ignacio
    5. Isaiah James de Dios Maling
    6. Joselito Torculas
    7. Rindell Mabunga
    8. Richard Phillip Dimaala Fernandez
    9. Melga Sonio
    10. Angelu G. Leynes
    11. Adrian Pilotos Burgos
    12. Russel J. Galanido
    13. Caed Mark Medul Mendoza
    14. Marvin Cato
    15. Sumet Ketsri
    16. Nixon Balandra
    17. Lilanie Monique Torilla
    18. Mark Elis Espiridion
    19. Jacob Sabido
    20. Christian Daang
    21. Emmanuel David
    22. Poetri Sonya Tarabunga
    23. Roenz Joshlee Timbol
    24. Ibrahim Demir
    25. Christian Paul Patawaran
    26. Amirul Faiz Abdul Muthalib
    27. Norwyn Nicholson Kah
    28. Chris Norman Algo
    29. Daniel James Molina
    30. Joem Canciller
    31. Jhepoy Dizon
    32. Ralph Macarasig
    33. John Marco Latagan
    34. Dreimuru Tempest
    35. Kurara Chibana
    36. Alea Astrea
    37. Kumar Ayush
    38. Lim Jing Ren
    39. Lenard Guillermo
    40. Mark Alvero
    41. Radu Bogo
    42. Randy Orton
    43. Willie Revillame Wowowin
 
9. Problem: 11C8 , proposed by Ahmet Arduc, Tip: Key Fact(s): 29D9
9 is the maximum number of cubes that are needed to sum to any positive integer.
If $a,b,c>0$ and $a+b+c=1$, what is the smallest value of $\frac{1}{a}+\frac{9}{b}+\frac{16}{c}\text{ ?}$ Ah Math

  • Correct answers have been submitted by:
    1. Jeffrey Robles
    2. Edge Ramos
    3. Joseph Rodelas
    4. Isaiah James de Dios Maling
    5. Joselito Torculas
    6. Rindell Mabunga
    7. Roenz Joshlee Timbol
    8. Marvin Cato
    9. Nheil Ignacio
    10. Melga Sonio
    11. Russel J. Galanido
    12. Sumet Ketsri
    13. Caed Mark Medul Mendoza
    14. Daniel James Molina
    15. Nixon Balandra
    16. Lilanie Monique Torilla
    17. Poetri Sonya Tarabunga
    18. Grant Lewis Bulaong
    19. Richard Phillip Dimaala Fernandez
    20. Christian Paul Patawaran
    21. Ibrahim Demir
    22. Amirul Faiz Abdul Muthalib
    23. Norwyn Nicholson Kah
    24. Ralph Macarasig
    25. Lenard Guillermo
    26. Kurara Chibana
    27. Kumar Ayush
    28. James Ericson
    29. Jacob Sabido
    30. Stefano Ongari
    31. Randy Orton
    32. Willie Revillame Wowowin
 
10. Problem: AC82 , proposed by Ahmet Arduc
10 is the only triangular number which is also the sum of 2 consecutive square odd numbers.
Find the value of the following expression.$$1\cdot2+3\cdot4+5\cdot6+\cdots+2017\cdot2018$$ Ah Math

  • Correct answers have been submitted by:
    1. Joseph Rodelas
    2. Jeffrey Robles
    3. Edge Ramos
    4. Isaiah James de Dios Maling
    5. John Albert A. Reyes
    6. Joselito Torculas
    7. Nheil Ignacio
    8. Rindell Mabunga
    9. Marvin Cato
    10. Russel J. Galanido
    11. Chris Norman Algo
    12. Angelu G. Leynes
    13. Melga Sonio
    14. Sumet Ketsri
    15. Nixon Balandra
    16. Caed Mark Medul Mendoza
    17. Lilanie Monique Torilla
    18. Richard Phillip Dimaala Fernandez
    19. Jacob Sabido
    20. Mark Elis Espiridion
    21. Emmanuel David
    22. Poetri Sonya Tarabunga
    23. Christian Paul Patawaran
    24. Ibrahim Demir
    25. Amirul Faiz Abdul Muthalib
    26. Daniel James Molina
    27. Joem Canciller
    28. Norwyn Nicholson Kah
    29. Jhepoy Dizon
    30. Fred Gutierrez
    31. Dreimuru Tempest
    32. Roenz Joshlee Timbol
    33. Kurara Chibana
    34. Lim Jing Ren
    35. Kumar Ayush
    36. Lenard Guillermo
    37. Radu Bogo
    38. Barry Villanueva
    39. Randy Orton
    40. Willie Revillame Wowowin
    41. Mertkan Simsek
 
11. Problem: C1B5 , proposed by Ahmet Arduc
11 is the only palindromic prime with an even number of digits.
What is the sum of the expression $2+3+5+8+13+\cdots+17711\text{ ?}$ Ah Math

  • Correct answers have been submitted by:
    1. John Gamal Aziz Attia
    2. Isaiah James de Dios Maling
    3. Chris Norman Algo
    4. Jeffrey Robles
    5. Joselito Torculas
    6. Melek Cimen
    7. Rindell Mabunga
    8. Angelu G. Leynes
    9. Melga Sonio
    10. Russel J. Galanido
    11. John Albert A. Reyes
    12. Nheil Ignacio
    13. Adrian Pilotos Burgos
    14. Caed Mark Medul Mendoza
    15. Marvin Cato
    16. Sumet Ketsri
    17. Daniel James Molina
    18. Lilanie Monique Torilla
    19. Nixon Balandra
    20. Jacob Sabido
    21. Mark Elis Espiridion
    22. Richard Phillip Dimaala Fernandez
    23. Christian Paul Patawaran
    24. Roenz Joshlee Timbol
    25. Ibrahim Demir
    26. Amirul Faiz Abdul Muthalib
    27. Norwyn Nicholson Kah
    28. Joem Canciller
    29. Ralph Macarasig
    30. Jhepoy Dizon
    31. John Marco Latagan
    32. Kurara Chibana
    33. Lim Jing Ren
    34. Kumar Ayush
    35. Gluttony
    36. Alea Astrea
    37. Randy Orton
    38. Willie Revillame Wowowin
    39. Mertkan Simsek
 
12. Problem: 24B8 , proposed by Ahmet Arduc
12 is the largest known even number expressible as the sum of two primes in one way.
In the following sequence, find the units digit of the 2017th term$$1,3,4,7,11,18, 29,47,...$$ Ah Math

  • Correct answers have been submitted by:
    1. Isaiah James de Dios Maling
    2. Jeffrey Robles
    3. Richard Phillip Dimaala Fernandez
    4. Joseph Rodelas
    5. Joselito Torculas
    6. Adrian Pilotos Burgos
    7. Rindell Mabunga
    8. Angelu G. Leynes
    9. Nheil Ignacio
    10. Russel J. Galanido
    11. Melga Sonio
    12. John Albert A. Reyes
    13. Caed Mark Medul Mendoza
    14. Marvin Cato
    15. Sumet Ketsri
    16. Nixon Balandra
    17. Daniel James Molina
    18. Lilanie Monique Torilla
    19. Jacob Sabido
    20. Emmanuel David
    21. Poetri Sonya Tarabunga
    22. Roenz Joshlee Timbol
    23. Christian Daang
    24. Christian Paul Patawaran
    25. Ibrahim Demir
    26. Amirul Faiz Abdul Muthalib
    27. Norwyn Nicholson Kah
    28. Joem Canciller
    29. Fred Gutierrez
    30. Ralph Macarasig
    31. Jhepoy Dizon
    32. Lim Jing Ren
    33. Lenard Guillermo
    34. Kurara Chibana
    35. James Ericson
    36. Alea Astrea
    37. Kumar Ayush
    38. Reymark Togno
    39. Gluttony
    40. Randy Orton
    41. Willie Revillame Wowowin
    42. Radu Bogo
 
13. Problem: 6392 , proposed by Ahmet Arduc
13 is the number of Archimedean solids.
Find the 2017th term of the sequence 1,2,1,1,3,1,1,1,4,1,1,1,1,5,... Ah Math

  • Correct answers have been submitted by:
    1. Sumet Ketsri
    2. Rindell Mabunga
    3. Russel J. Galanido
    4. Joselito Torculas
    5. Nheil Ignacio
    6. Richard Phillip Dimaala Fernandez
    7. Marvin Cato
    8. Jeffrey Robles
    9. Angelu G. Leynes
    10. Caed Mark Medul Mendoza
    11. Isaiah James de Dios Maling
    12. Nixon Balandra
    13. Daniel James Molina
    14. Lilanie Monique Torilla
    15. Jacob Sabido
    16. Mark Elis Espiridion
    17. Christian Daang
    18. John Albert A. Reyes
    19. Emmanuel David
    20. Poetri Sonya Tarabunga
    21. Christian Paul Patawaran
    22. Roenz Joshlee Timbol
    23. Ibrahim Demir
    24. Amirul Faiz Abdul Muthalib
    25. Joem Canciller
    26. Norwyn Nicholson Kah
    27. Fred Gutierrez
    28. Ralph Macarasig
    29. Jhepoy Dizon
    30. Lim Jing Ren
    31. John Marco Latagan
    32. Hanelet Santos
    33. Mark Alvero
    34. Kurara Chibana
    35. Alea Astrea
    36. Lenard Guillermo
    37. Gluttony
    38. Reymark Togno
    39. Radu Bogo
    40. Stefano Ongari
    41. Randy Orton
    42. Willie Revillame Wowowin
 
14. Problem: 615D , proposed by Ahmet Arduc
14 is the smallest even number n with no solutions to φ(m) = n.
Evaluate the following expression: $$1\cdot 2\cdot 3+2\cdot 3\cdot 4+3\cdot 4\cdot 5 \,+...+\,31\cdot 32\cdot 33$$ Ah Math

  • Correct answers have been submitted by:
    1. Russel J. Galanido
    2. Rindell Mabunga
    3. Richard Phillip Dimaala Fernandez
    4. Joselito Torculas
    5. Jeffrey Robles
    6. Isaiah James de Dios Maling
    7. Caed Mark Medul Mendoza
    8. Nheil Ignacio
    9. John Albert A. Reyes
    10. Lilanie Monique Torilla
    11. Nixon Balandra
    12. Jacob Sabido
    13. Mark Elis Espiridion
    14. Chris Norman Algo
    15. Marvin Cato
    16. Poetri Sonya Tarabunga
    17. Christian Paul Patawaran
    18. Christian Daang
    19. Ibrahim Demir
    20. Amirul Faiz Abdul Muthalib
    21. Roenz Joshlee Timbol
    22. Daniel James Molina
    23. Joem Canciller
    24. Norwyn Nicholson Kah
    25. Ralph Macarasig
    26. Jhepoy Dizon
    27. Sumet Ketsri
    28. John Marco Latagan
    29. Fred Gutierrez
    30. Kurara Chibana
    31. Lim Jing Ren
    32. James Ericson
    33. Alea Astrea
    34. Kumar Ayush
    35. Lenard Guillermo
    36. Radu Bogo
    37. Randy Orton
    38. Willie Revillame Wowowin
    39. Mertkan Simsek
 
15. Problem: A836 , proposed by Ahmet Arduc
15 is the number of 3-digit palindromic primes.
Let $A=2016+2017$. How many proper irreducible positive fractions are there whose denominator is $A$? Ah Math

  • Correct answers have been submitted by:
    1. John Gamal Aziz Attia
    2. Jeffrey Robles
    3. Joselito Torculas
    4. Russel J. Galanido
    5. Jacob Sabido
    6. Marvin Cato
    7. Nixon Balandra
    8. Christian Daang
    9. John Albert A. Reyes
    10. Poetri Sonya Tarabunga
    11. Richard Phillip Dimaala Fernandez
    12. Rindell Mabunga
    13. Kimi No Nawa
    14. Caed Mark Medul Mendoza
    15. Lilanie Monique Torilla
    16. Roenz Joshlee Timbol
    17. Isaiah James de Dios Maling
    18. Christian Paul Patawaran
    19. Ibrahim Demir
    20. Amirul Faiz Abdul Muthalib
    21. Norwyn Nicholson Kah
    22. Daniel James Molina
    23. John Rocel Perez
    24. Ralph Macarasig
    25. Jhepoy Dizon
    26. Sumet Ketsri
    27. Kurara Chibana
    28. Lim Jing Ren
    29. James Ericson
    30. Alea Astrea
    31. Kumar Ayush
    32. Stefano Ongari
 
16. Problem: 7B83 , proposed by Ahmet Arduc
2017 is palindromic in base 31: 232.
Let $a+b+c=0$. find the value of $$a\cdot\left(\frac{1}{b}+\frac{1}{c}+1\right)+b\cdot\left(\frac{1}{c}+\frac{1}{a}+1\right)+c\cdot\left(\frac{1}{a}+\frac{1}{b}+1\right)+2017$$ Ah Math

  • Correct answers have been submitted by:
    1. Richard Phillip Dimaala Fernandez
    2. Joselito Torculas
    3. Nixon Balandra
    4. Jeffrey Robles
    5. Jacob Sabido
    6. Marvin Cato
    7. Nheil Ignacio
    8. Russel J. Galanido
    9. Caed Mark Medul Mendoza
    10. Lilanie Monique Torilla
    11. Rindell Mabunga
    12. Daniel James Molina
    13. Roenz Joshlee Timbol
    14. Christian Daang
    15. Isaiah James de Dios Maling
    16. Christian Paul Patawaran
    17. Kimi No Nawa
    18. Ibrahim Demir
    19. Amirul Faiz Abdul Muthalib
    20. Norwyn Nicholson Kah
    21. Joem Canciller
    22. John Lester Tan
    23. John Rocel Perez
    24. Ralph Macarasig
    25. Jhepoy Dizon
    26. Lim Jing Ren
    27. Sumet Ketsri
    28. Sigmund Dela Cruz
    29. Srinivas Kanigiri
    30. Kurara Chibana
    31. James Ericson
    32. Alea Astrea
    33. Kumar Ayush
    34. Radu Bogo
    35. Stefano Ongari
    36. Randy Orton
    37. Willie Revillame Wowowin
    38. Evan Gruda
 
17. Problem: E328 , proposed by Ahmet Arduc
17 is the number of wallpaper groups.
In the matrix given below, if there are $x$ numbers above 2017 and $y$ numbers to the left of 2017, what is the sum of $x$ and $y$ $?$ $$\matrix{1 & 4 & 5 & 16 & 17 & \cdots \cr 2 & 3 & 6 & 15 & 18 & \cdots \cr 9 & 8 & 7 & 14 & 19 & \cdots \cr 10 & 11 & 12 & 13 & 20 & \cdots \cr 25 & 24 & 23 & 22 & 21 & \cdots \cr 26 & \cdots & \cdots & \cdots & \cdots & \cdots}$$ Ah Math

  • Correct answers have been submitted by:
    1. Kimi No Nawa
    2. Caed Mark Medul Mendoza
    3. Lilanie Monique Torilla
    4. Nixon Balandra
    5. Joselito Torculas
    6. Marvin Cato
    7. Rindell Mabunga
    8. Richard Phillip Dimaala Fernandez
    9. Russel J. Galanido
    10. Jacob Sabido
    11. Isaiah James de Dios Maling
    12. Christian Daang
    13. Chris Norman Algo
    14. Amirul Faiz Abdul Muthalib
    15. Daniel James Molina
    16. Christian Paul Patawaran
    17. Joem Canciller
    18. Norwyn Nicholson Kah
    19. Jeffrey Robles
    20. Jhepoy Dizon
    21. Lim Jing Ren
    22. Hanelet Santos
    23. Sumet Ketsri
    24. Roenz Joshlee Timbol
    25. Kurara Chibana
    26. James Ericson
    27. Stefano Ongari
    28. Randy Orton
    29. Willie Revillame Wowowin
 
18. Problem: B613 , proposed by Ahmet Arduc
1971 is the birth year of A. Arduc.
Find the remainder when $1^{1971}+2^{1971}+3^{1971}+...+2016^{1971}$ is divided by $2017$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Marvin Cato
    2. Joselito Torculas
    3. Rindell Mabunga
    4. Jacob Sabido
    5. Russel J. Galanido
    6. Richard Phillip Dimaala Fernandez
    7. Nixon Balandra
    8. Roenz Joshlee Timbol
    9. Isaiah James de Dios Maling
    10. Grant Lewis Bulaong
    11. Kimi No Nawa
    12. Lilanie Monique Torilla
    13. Caed Mark Medul Mendoza
    14. Christian Paul Patawaran
    15. Jeffrey Robles
    16. Ibrahim Demir
    17. Christian Daang
    18. Amirul Faiz Abdul Muthalib
    19. Norwyn Nicholson Kah
    20. Chris Norman Algo
    21. Daniel James Molina
    22. John Lester Tan
    23. Ralph Macarasig
    24. Jhepoy Dizon
    25. Sumet Ketsri
    26. Nheil Ignacio
    27. Sigmund Dela Cruz
    28. Srinivas Kanigiri
    29. Kurara Chibana
    30. Alea Astrea
    31. Lim Jing Ren
    32. Kumar Ayush
    33. Randy Orton
    34. Willie Revillame Wowowin
    35. Radu Bogo
    36. Mertkan Simsek
 
19. Problem: EE2C , proposed by Ahmet Arduc
351 is the sum of five consecutive prime numbers: 61 + 67 + 71 + 73 + 79.
By using only letters of English alphabet, label one marble 'A', two marbles 'B', three marbles 'C',..., twenty-six marbles 'Z'. Put these$$1+2+3+\cdots+26=351$$labeled marbles in a bag. Marbles are then drawn from the bag at random without replacement. What is the minimum number of marbles that must be drawn to guarantee drawing at least ten marbles with the same label? Ah Math

  • Correct answers have been submitted by:
    1. Joselito Torculas
    2. Rindell Mabunga
    3. Nixon Balandra
    4. Russel J. Galanido
    5. Richard Phillip Dimaala Fernandez
    6. Marvin Cato
    7. Jacob Sabido
    8. Kimi No Nawa
    9. Caed Mark Medul Mendoza
    10. Lilanie Monique Torilla
    11. Jeffrey Robles
    12. Sumet Ketsri
    13. Isaiah James de Dios Maling
    14. Christian Paul Patawaran
    15. Christian Daang
    16. Amirul Faiz Abdul Muthalib
    17. Norwyn Nicholson Kah
    18. Daniel James Molina
    19. Joem Canciller
    20. Ralph Macarasig
    21. Jhepoy Dizon
    22. Lim Jing Ren
    23. Mark Alvero
    24. Roenz Joshlee Timbol
    25. Kurara Chibana
    26. Kumar Ayush
    27. Reymark Togno
    28. Gluttony
    29. Alea Astrea
    30. Radu Bogo
 
20. Problem: E4C6 , proposed by Ahmet Arduc, Tip: Key Fact(s): 8632
1017 is the smallest number whose square contains 7 different digits.
Find the remainder when $1001\times1002\times1003\times...\times2017$ is divided by $1017!$. Ah Math

  • Correct answers have been submitted by:
    1. Kimi No Nawa
    2. Caed Mark Medul Mendoza
    3. Lilanie Monique Torilla
    4. Joselito Torculas
    5. Russel J. Galanido
    6. Jacob Sabido
    7. Rindell Mabunga
    8. Nixon Balandra
    9. Richard Phillip Dimaala Fernandez
    10. Isaiah James de Dios Maling
    11. Christian Paul Patawaran
    12. Ibrahim Demir
    13. Roenz Joshlee Timbol
    14. Amirul Faiz Abdul Muthalib
    15. Daniel James Molina
    16. Norwyn Nicholson Kah
    17. Jeffrey Robles
    18. Jhepoy Dizon
    19. Ralph Macarasig
    20. Sumet Ketsri
    21. Marvin Cato
    22. Sigmund Dela Cruz
    23. Kurara Chibana
    24. Alea Astrea
    25. Lim Jing Ren
    26. Christian Daang
    27. Kumar Ayush
    28. Lenard Guillermo
    29. Radu Bogo
    30. Randy Orton
    31. Willie Revillame Wowowin
    32. Mertkan Simsek
 
21. Problem: ABBA , proposed by Ahmet Arduc
21 is the smallest number of distinct squares needed to tile a square.
How many pairs of distinct integers between 1 and 2017 inclusively have their products as multiple of 6? Ah Math

  • Correct answers have been submitted by:
    1. Russel J. Galanido
    2. Isaiah James de Dios Maling
    3. Rindell Mabunga
    4. Caed Mark Medul Mendoza
    5. Amirul Faiz Abdul Muthalib
    6. Lilanie Monique Torilla
    7. Nixon Balandra
    8. Richard Phillip Dimaala Fernandez
    9. Daniel James Molina
    10. Christian Paul Patawaran
    11. Norwyn Nicholson Kah
    12. Jeffrey Robles
    13. Joselito Torculas
    14. Jhepoy Dizon
    15. Lim Jing Ren
    16. Marvin Cato
    17. Sumet Ketsri
    18. Ikemen
 
22. Problem: DAB1 , proposed by Ahmet Arduc
1971 is the birth year of A. Arduc.
An integer $x$ plus 1971 is the square of a positive integer, and $x$ minus 46 is the square of another positive integer. Find the value of $x$. Ah Math

  • Correct answers have been submitted by:
    1. Rindell Mabunga
    2. Russel J. Galanido
    3. Roenz Joshlee Timbol
    4. Amirul Faiz Abdul Muthalib
    5. Caed Mark Medul Mendoza
    6. Lilanie Monique Torilla
    7. Isaiah James de Dios Maling
    8. Nixon Balandra
    9. Richard Phillip Dimaala Fernandez
    10. Christian Paul Patawaran
    11. Daniel James Molina
    12. Joem Canciller
    13. Norwyn Nicholson Kah
    14. Joselito Torculas
    15. Jeffrey Robles
    16. Ralph Macarasig
    17. Jhepoy Dizon
    18. Lim Jing Ren
    19. Sumet Ketsri
    20. Marvin Cato
    21. Hanelet Santos
    22. Srinivas Kanigiri
    23. Kurara Chibana
    24. James Ericson
    25. Alea Astrea
    26. Kumar Ayush
    27. Lenard Guillermo
    28. Gluttony
    29. Jacob Sabido
    30. Radu Bogo
    31. Mark Alvero
    32. Stefano Ongari
    33. Randy Orton
    34. Willie Revillame Wowowin
 
23. Problem: D36C , proposed by Ahmet Arduc
23 is the smallest odd prime which is not a twin prime.
Let $x$ be a real number and$$A=\sqrt{x^2-26x+170}+\sqrt{x^2-52x+1700}.$$What is the square of the minimum value of $A$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Isaiah James de Dios Maling
    3. Daniel James Molina
    4. Richard Phillip Dimaala Fernandez
    5. Rindell Mabunga
    6. Norwyn Nicholson Kah
    7. John Lester Tan
    8. Joselito Torculas
    9. Jeffrey Robles
    10. Ralph Macarasig
    11. Jhepoy Dizon
    12. Kimi No Nawa
    13. Caed Mark Medul Mendoza
    14. Lilanie Monique Torilla
    15. Nixon Balandra
    16. Russel J. Galanido
    17. Jacob Sabido
    18. Marvin Cato
    19. Sumet Ketsri
    20. Sigmund Dela Cruz
    21. Christian Daang
    22. Kurara Chibana
    23. Joem Canciller
    24. Gluttony
    25. Randy Orton
    26. Willie Revillame Wowowin
 
24. Problem: D7C4 , proposed by Ahmet Arduc
The product of 4 consecutive numbers n(n+1)(n+2)(n+3) is divisible by 24.
How many $x$ values are there which makes $\sqrt{2017-\sqrt{x}}$ an integer? Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Norwyn Nicholson Kah
    3. Kimi No Nawa
    4. Isaiah James de Dios Maling
    5. Joselito Torculas
    6. Daniel James Molina
    7. Jeffrey Robles
    8. Richard Phillip Dimaala Fernandez
    9. Ralph Macarasig
    10. Rindell Mabunga
    11. Caed Mark Medul Mendoza
    12. Lilanie Monique Torilla
    13. Jhepoy Dizon
    14. Nixon Balandra
    15. Russel J. Galanido
    16. Lim Jing Ren
    17. Sumet Ketsri
    18. Marvin Cato
    19. Mark Alvero
    20. John Albert A. Reyes
    21. Roenz Joshlee Timbol
    22. Smahi Abdeslem
    23. Srinivas Kanigiri
    24. Kurara Chibana
    25. James Ericson
    26. Afshiram Muhammed
    27. Alea Astrea
    28. Jacob Sabido
    29. Kumar Ayush
    30. Lenard Guillermo
    31. Serdal Aslantas
    32. Radu Bogo
 
25. Problem: A4C5 , proposed by Ahmet Arduc, Tip: Key Fact(s): 7695
25 is the smallest square number that can be written as a sum of 2 consecutive squares.
$$A=\left(1-\frac{1}{2^2}\right)\cdot\left(1-\frac{1}{3^2}\right)\cdot...\cdot\left(1-\frac{1}{2017^2}\right)$$If $A$ is written in its simplest form as $\frac{a}{b}$, what is the sum of $a$ and $b$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Joselito Torculas
    3. Jeffrey Robles
    4. Norwyn Nicholson Kah
    5. Richard Phillip Dimaala Fernandez
    6. Sumet Ketsri
    7. Ralph Macarasig
    8. Kimi No Nawa
    9. Rindell Mabunga
    10. Caed Mark Medul Mendoza
    11. Lilanie Monique Torilla
    12. Nixon Balandra
    13. Isaiah James de Dios Maling
    14. Russel J. Galanido
    15. Jhepoy Dizon
    16. Lim Jing Ren
    17. Daniel James Molina
    18. Jacob Sabido
    19. Marvin Cato
    20. Fred Gutierrez
    21. Nheil Ignacio
    22. John Albert A. Reyes
    23. Srinivas Kanigiri
    24. Chris Norman Algo
    25. Kurara Chibana
    26. Kumar Ayush
    27. Joem Canciller
    28. Gluttony
    29. Reymark Togno
    30. Roenz Joshlee Timbol
    31. Mark Alvero
    32. Radu Bogo
    33. Randy Orton
    34. Willie Revillame Wowowin
 
26. Problem: A378 , proposed by Ahmet Arduc
1953 is a Kaprekar constant in base 2.
Find the sum of all real numbers $x$ for which$$1953^x+1954^x+...+1984^x=1985^x+1986^x+...+2015^x.$$ Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Isaiah James de Dios Maling
    3. Joselito Torculas
    4. Jhepoy Dizon
    5. Jeffrey Robles
    6. Ralph Macarasig
    7. Norwyn Nicholson Kah
    8. Daniel James Molina
    9. Richard Phillip Dimaala Fernandez
    10. Russel J. Galanido
    11. Kimi No Nawa
    12. Caed Mark Medul Mendoza
    13. Lilanie Monique Torilla
    14. Marvin Cato
    15. Nixon Balandra
    16. Rindell Mabunga
    17. Kurara Chibana
    18. Sumet Ketsri
    19. Kumar Ayush
    20. Lenard Guillermo
    21. Randy Orton
    22. Willie Revillame Wowowin
 
27. Problem: 3DC5 , proposed by Ahmet Arduc
27 is the largest integer which is the sum of the digits of its cube.
Find the coefficient of $x^2$ when$$\left(1+x\right)\left(1+2x\right)\left(1+4x\right)\cdots\left(1+2^9x\right)$$is expanded $?$ Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Isaiah James de Dios Maling
    3. Richard Phillip Dimaala Fernandez
    4. Joselito Torculas
    5. Russel J. Galanido
    6. Sumet Ketsri
    7. Caed Mark Medul Mendoza
    8. Lilanie Monique Torilla
    9. Daniel James Molina
    10. Marvin Cato
    11. Hanelet Santos
    12. Jacob Sabido
    13. Rindell Mabunga
    14. Nixon Balandra
    15. Jeffrey Robles
    16. Sigmund Dela Cruz
    17. Kurara Chibana
    18. James Ericson
    19. Alea Astrea
    20. Randy Orton
    21. Willie Revillame Wowowin
 
28. Problem: 9E31 , proposed by Ahmet Arduc, Tip: Key Fact(s): 7695
30 is the 4th pyramidal number.
For how many rational numbers between 0 and 1, written as a fraction in its lowest terms, the product of its numerator and denominator will be $30!$. Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Russel J. Galanido
    3. Marvin Cato
    4. Daniel James Molina
    5. Joselito Torculas
    6. Isaiah James de Dios Maling
    7. Richard Phillip Dimaala Fernandez
    8. Kimi No Nawa
    9. Caed Mark Medul Mendoza
    10. Rindell Mabunga
    11. Nixon Balandra
    12. Sumet Ketsri
    13. Roenz Joshlee Timbol
    14. Smahi Abdeslem
    15. Kurara Chibana
    16. Lenard Guillermo
    17. Lilanie Monique Torilla
 
29. Problem: EEAA , proposed by Ahmet Arduc
255 equals 11111111 in base 2.
The increasing sequence 1, 3, 4, 9, 10, 12, 13,... consists of all positive integers which are powers of 3 or sums of distinct powers of 3. What is the 255th term of this sequence? Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Russel J. Galanido
    3. Sumet Ketsri
    4. Jacob Sabido
    5. Joselito Torculas
    6. Marvin Cato
    7. Richard Phillip Dimaala Fernandez
    8. Isaiah James de Dios Maling
    9. Daniel James Molina
    10. Caed Mark Medul Mendoza
    11. Nixon Balandra
    12. Rindell Mabunga
    13. Jeffrey Robles
    14. Dreimuru Tempest
    15. Roenz Joshlee Timbol
    16. Kurara Chibana
    17. Lim Jing Ren
    18. Kumar Ayush
    19. Stefano Ongari
    20. Randy Orton
    21. Willie Revillame Wowowin
 
30. Problem: 442B , proposed by Ahmet Arduc
30 is the largest number such that every smaller coprime to it is prime.
What is the sum of the first 2017 terms of the given sequence?$$\style{color:red}1,1,\style{color:red}1,1,2,\style{color:red}1,1,2,3,\style{color:red}1,1,2,3,4,\style{color:red}1,1,2,3,4,5,\style{color:red}1,...$$ Ah Math

  • Correct answers have been submitted by:
    1. Joselito Torculas
    2. Sumet Ketsri
    3. Amirul Faiz Abdul Muthalib
    4. Marvin Cato
    5. Nixon Balandra
    6. Caed Mark Medul Mendoza
    7. Isaiah James de Dios Maling
    8. Richard Phillip Dimaala Fernandez
    9. Daniel James Molina
    10. Jeffrey Robles
    11. Jacob Sabido
    12. Dreimuru Tempest
    13. Russel J. Galanido
    14. Kurara Chibana
    15. Lim Jing Ren
    16. Rindell Mabunga
    17. Roenz Joshlee Timbol
    18. Stefano Ongari
    19. Randy Orton
    20. Willie Revillame Wowowin
 
31. Problem: B854 , proposed by Ahmet Arduc, Tip: Key Fact(s): A031878.
The sum of the first 31 odd primes is a perfect square.
Let $S$ be a square. There are five distinct circles in the plane of $S$ which have a diameter both of whose endpoints are vertices of $S$. Let $T$ be a 2017-sided regular polygon. How many distinct circles in the plane of $T$ have a diameter both of whose endpoints are vertices of $T$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Dreimuru Tempest
    2. Amirul Faiz Abdul Muthalib
    3. Nixon Balandra
    4. Richard Phillip Dimaala Fernandez
    5. Joselito Torculas
    6. Marvin Cato
    7. Isaiah James de Dios Maling
    8. Sumet Ketsri
    9. Kimi No Nawa
    10. Caed Mark Medul Mendoza
    11. Kurara Chibana
    12. Russel J. Galanido
    13. Rindell Mabunga
    14. Lim Jing Ren
    15. Jeffrey Robles
    16. Randy Orton
    17. Willie Revillame Wowowin
 
32. Problem: 95E3 , proposed by Ahmet Arduc
32 the largest known power with all decimal digits being prime.
8 points on a circle are numbered 0, 1, 2,..., 6, and 7 in counter clockwise order. A ladybug moves in a counter-clockwise direction from one point to another, starting from point 0, 1 point in its first move, 2 points in its second move, 3 points in its third move, and so on. Thus, it will be on point 1 after its first move, on point 3 after its second move, on point 6 after its third move, and so on. On which point, will it be after its 2017th move? Ah Math

  • Correct answers have been submitted by:
    1. Joselito Torculas
    2. Richard Phillip Dimaala Fernandez
    3. Nixon Balandra
    4. Jacob Sabido
    5. Amirul Faiz Abdul Muthalib
    6. Daniel James Molina
    7. Isaiah James de Dios Maling
    8. Marvin Cato
    9. Sumet Ketsri
    10. Roenz Joshlee Timbol
    11. Kimi No Nawa
    12. Caed Mark Medul Mendoza
    13. Chris Norman Algo
    14. Russel J. Galanido
    15. Kurara Chibana
    16. Rindell Mabunga
    17. Lim Jing Ren
    18. Jeffrey Robles
    19. Joem Canciller
    20. Gluttony
    21. Stefano Ongari
    22. Mark Alvero
    23. Randy Orton
    24. Willie Revillame Wowowin
 
33. Problem: 3E1C , proposed by Ahmet Arduc
33 is the largest number that is not a sum of distinct triangular numbers.
What is the sum of the first digits (not the units digits) of all powers of 2, from $2^0$ to $2^{2017}$ inclusive $?$ Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Joselito Torculas
    3. Isaiah James de Dios Maling
    4. Richard Phillip Dimaala Fernandez
    5. Marvin Cato
    6. Nixon Balandra
    7. Jacob Sabido
    8. Russel J. Galanido
    9. Kurara Chibana
    10. Caed Mark Medul Mendoza
    11. Rindell Mabunga
    12. Lim Jing Ren
 
34. Problem: 1715 , proposed by Ahmet Arduc
1910 is the birth year of Cahit Arf.
Let $O(n)$ denote the sum of the odd digits of $n$. For example, $O(1910)=1+9+1=11$. What is the sum of$$O(1)+O(2)+O(3)+...+O(2017)$$ Ah Math

  • Correct answers have been submitted by:
    1. Ikemen
    2. Smahi Abdeslem
    3. Russel J. Galanido
    4. Sumet Ketsri
    5. Nixon Balandra
    6. Richard Phillip Dimaala Fernandez
    7. Joselito Torculas
    8. Marvin Cato
    9. Isaiah James de Dios Maling
    10. Amirul Faiz Abdul Muthalib
    11. Kimi No Nawa
    12. Caed Mark Medul Mendoza
    13. Kurara Chibana
    14. Rindell Mabunga
    15. Roenz Joshlee Timbol
    16. Jeffrey Robles
 
35. Problem: C877 , proposed by Ahmet Arduc
35 is the number of hexominoes.
The sequence $u_1, u_2, u_3,...$ satisfies $u_1=1$, $u_{2017}=2017$, and, for all $n\ge3$, $u_n$ is the average (arithmetic mean) of the first $n-1$ terms. What is the sum of the first three terms? Ah Math

  • Correct answers have been submitted by:
    1. Dreimuru Tempest
    2. Andrew Chiu
    3. Marvin Cato
    4. Ikemen
    5. Richard Phillip Dimaala Fernandez
    6. Isaiah James de Dios Maling
    7. Joselito Torculas
    8. Jacob Sabido
    9. Russel J. Galanido
    10. Nixon Balandra
    11. Sumet Ketsri
    12. Amirul Faiz Abdul Muthalib
    13. Kurara Chibana
    14. Rindell Mabunga
    15. Kimi No Nawa
    16. Caed Mark Medul Mendoza
    17. Alea Astrea
    18. Lim Jing Ren
    19. Kumar Ayush
    20. Jeffrey Robles
    21. Joem Canciller
    22. Gluttony
    23. Randy Orton
    24. Willie Revillame Wowowin
 
36. Problem: C2BC , proposed by Ahmet Arduc
36 is the smallest number which is the sum of pairs of distinct odd primes in four ways.
A piece of graph paper is folded once so that $(2, 1)$ is matched with $(0, 5)$. If $(a, b)$ is matched with itself where $a+b=2017$, what is the value of $a$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Ikemen
    2. Isaiah James de Dios Maling
    3. Jacob Sabido
    4. Caed Mark Medul Mendoza
    5. Nixon Balandra
    6. Amirul Faiz Abdul Muthalib
    7. Richard Phillip Dimaala Fernandez
    8. Marvin Cato
    9. Andrew Chiu
    10. Joselito Torculas
    11. Russel J. Galanido
    12. Sumet Ketsri
    13. Kurara Chibana
    14. Alea Astrea
    15. Rindell Mabunga
    16. Jeffrey Robles
    17. Kumar Ayush
    18. Joem Canciller
    19. Gluttony
    20. Mark Alvero
    21. Randy Orton
    22. Willie Revillame Wowowin
 
37. Problem: E4AE , proposed by Ahmet Arduc
37 is the maximum number of 5th powers needed to sum to any number.
For the sets of consecutive integers $$\{1\}, \{2, 3\}, \{4, 5, 6\}, \{7, 8, 9, 10\},...$$ let $S_n$ be the sum of the elements in the $n$th set. What is the remainder when $S_{2017}$ is divided by $9$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Ikemen
    2. Richard Phillip Dimaala Fernandez
    3. Kurara Chibana
    4. Isaiah James de Dios Maling
    5. Russel J. Galanido
    6. Marvin Cato
    7. Amirul Faiz Abdul Muthalib
    8. Joselito Torculas
    9. Smahi Abdeslem
    10. Jacob Sabido
    11. Alea Astrea
    12. Nixon Balandra
    13. Sumet Ketsri
    14. Lim Jing Ren
    15. Rindell Mabunga
    16. Kimi No Nawa
    17. Caed Mark Medul Mendoza
    18. Jeffrey Robles
    19. Lenard Guillermo
    20. Joem Canciller
    21. Gluttony
    22. Stefano Ongari
    23. Randy Orton
    24. Willie Revillame Wowowin
 
38. Problem: 57BD , proposed by Ahmet Arduc
38 is the largest known even number which can be represented as sum of two distinct primes in only one way.
What is the remainder when the sum of the first 2017 terms of the sequence$$1,\hspace{0.2cm}1+2,\hspace{0.2cm}1+2+2^2,...,\hspace{0.2cm}1+2+2^2+...+2^{n-1},...$$is divided by 9 $?$ Ah Math

  • Correct answers have been submitted by:
    1. Sumet Ketsri
    2. James Ericson
    3. Andrew Chiu
    4. Joselito Torculas
    5. Richard Phillip Dimaala Fernandez
    6. Caed Mark Medul Mendoza
    7. Isaiah James de Dios Maling
    8. Nixon Balandra
    9. Jeffrey Robles
    10. Marvin Cato
    11. Amirul Faiz Abdul Muthalib
    12. Lim Jing Ren
    13. Jacob Sabido
    14. Rindell Mabunga
    15. Alea Astrea
    16. Kurara Chibana
    17. Russel J. Galanido
    18. Roenz Joshlee Timbol
    19. Mark Alvero
    20. Randy Orton
    21. Radu Bogo
    22. Willie Revillame Wowowin
 
39. Problem: 3785 , proposed by Ahmet Arduc
39 is the smallest number which has 3 different partitions into 3 parts with the same product.
$428$ has the property that its square appears as two consecutive integers:$$428^2=183184$$What is the sum of all 3-digit numbers with this property? Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Andrew Chiu
    3. Nixon Balandra
    4. Caed Mark Medul Mendoza
    5. Marvin Cato
    6. Joselito Torculas
    7. Rindell Mabunga
    8. Isaiah James de Dios Maling
    9. Richard Phillip Dimaala Fernandez
    10. Kurara Chibana
    11. Russel J. Galanido
    12. James Ericson
    13. Alea Astrea
    14. Jacob Sabido
    15. Sumet Ketsri
    16. Lim Jing Ren
    17. Jeffrey Robles
    18. Randy Orton
    19. Willie Revillame Wowowin
 
40. Problem: 2783 , proposed by Ahmet Arduc
40 is a pentagonal pyramidal number.
What is the greatest number less than 2017, when divided by the sum of its digits gives the greatest remainder? Ah Math

  • Correct answers have been submitted by:
    1. Nixon Balandra
    2. Isaiah James de Dios Maling
    3. Marvin Cato
    4. Andrew Chiu
    5. Amirul Faiz Abdul Muthalib
    6. Joselito Torculas
    7. Rindell Mabunga
    8. Caed Mark Medul Mendoza
    9. Lilanie Monique Torilla
    10. Richard Phillip Dimaala Fernandez
    11. Kurara Chibana
    12. Russel J. Galanido
    13. James Ericson
    14. Sumet Ketsri
    15. Alea Astrea
    16. Jacob Sabido
    17. Jeffrey Robles
    18. Joem Canciller
    19. Gluttony
    20. Randy Orton
    21. Willie Revillame Wowowin
 
41. Problem: 398B , proposed by Ahmet Arduc
41 is the lowest number whose cube is the sum of 3 cube numbers in 2 different ways.
The numbers$$1,\frac{1}{2},\frac{1}{3},\frac{1}{4},...,\frac{1}{2016},\frac{1}{2017}$$are all written on a board. Two numbers $x$ and $y$ are selected randomly from the list, deleted, and replaced by the single number $x+y+x\cdot y$. This is done repeatedly until one number is left. What is the last number remaining on the board? Ah Math

  • Correct answers have been submitted by:
    1. Isaiah James de Dios Maling
    2. Nixon Balandra
    3. Kurara Chibana
    4. Russel J. Galanido
    5. Rindell Mabunga
    6. Marvin Cato
    7. James Ericson
    8. Andrew Chiu
    9. Ikemen
    10. Caed Mark Medul Mendoza
    11. Sumet Ketsri
    12. Joselito Torculas
    13. Alea Astrea
    14. Richard Phillip Dimaala Fernandez
    15. Jacob Sabido
    16. Amirul Faiz Abdul Muthalib
    17. Lim Jing Ren
    18. Jeffrey Robles
    19. Lenard Guillermo
    20. Joem Canciller
    21. Gluttony
    22. Stefano Ongari
    23. Mark Alvero
    24. Randy Orton
    25. Willie Revillame Wowowin
 
42. Problem: DE1D , proposed by Ahmet Arduc
42 is the he smallest perfect square that is the mean of two cubed twin primes.
Let $ABC$ be a triangle. $E \in [BC]$. If $|AB|=32$, $|BE|=16$, $|EC|=48$, and $m(BCA)=24^{\circ}$, what is the measure of the angle $EAB$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Sumet Ketsri
    2. Kurara Chibana
    3. Russel J. Galanido
    4. Marvin Cato
    5. Rindell Mabunga
    6. Ikemen
    7. Richard Phillip Dimaala Fernandez
    8. Isaiah James de Dios Maling
    9. Nixon Balandra
    10. Kimi No Nawa
    11. Amirul Faiz Abdul Muthalib
    12. Caed Mark Medul Mendoza
    13. Jeffrey Robles
    14. Lilanie Monique Torilla
    15. Joem Canciller
    16. Gluttony
    17. Andrew Chiu
    18. Roenz Joshlee Timbol
    19. Randy Orton
    20. Willie Revillame Wowowin
 
43. Problem: B87D , proposed by Ahmet Arduc
43 is the smallest non-palindromic prime which on subtracting its reverse gives a perfect square.
Let $ABC$ be a triangle. Let $D$ be a point in the interior of $ABC$, such that, $|AD|=|DB|$. If $m(DBA)=11^{\circ}$, $m(DBC)=38^{\circ}$, and $m(DAC)=19^{\circ}$, what is the measure of the angle $m(DCA)$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Kurara Chibana
    2. Russel J. Galanido
    3. Amirul Faiz Abdul Muthalib
    4. Kimi No Nawa
    5. Caed Mark Medul Mendoza
    6. Marvin Cato
    7. Rindell Mabunga
    8. Sumet Ketsri
    9. Jeffrey Robles
    10. Lim Jing Ren
    11. Lilanie Monique Torilla
    12. Andrew Chiu
    13. Isaiah James de Dios Maling
    14. Randy Orton
    15. Willie Revillame Wowowin
 
44. Problem: C426 , proposed by Amirul Faiz Abdul Muthalib
44 is the number of derangements of 5 objects.
Let $P(x)$ be a polynomial where $deg(P(x))=2015$. If $P(0)=1$, $P(1)=2$, $P(2)=3$, ..., $P(2013)=2014$, and $P(2014)=2015$, but $P(2015)=2017$, what is the value of $P(2017)$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Christian Daang
    2. Sumet Ketsri
    3. Kumar Ayush
    4. Rindell Mabunga
    5. Kurara Chibana
    6. Russel J. Galanido
    7. Marvin Cato
    8. Jeffrey Robles
    9. Nixon Balandra
    10. Isaiah James de Dios Maling
    11. Richard Phillip Dimaala Fernandez
    12. Kimi No Nawa
    13. Caed Mark Medul Mendoza
    14. Lilanie Monique Torilla
    15. Roenz Joshlee Timbol
    16. Randy Orton
    17. Willie Revillame Wowowin
 
45. Problem: 143B , proposed by Amirul Faiz Abdul Muthalib
45 is both a Kaprekar and a triangular number.
Ahmet added up all the odd integers from $1$ to a certain number on his calculator and obtained a sum of $2017$. Unfortunately, he mistakenly entered one of the numbers twice. What is the number that he added twice? Ah Math

  • Correct answers have been submitted by:
    1. Richard Phillip Dimaala Fernandez
    2. Kumar Ayush
    3. Nixon Balandra
    4. Kurara Chibana
    5. Russel J. Galanido
    6. Caed Mark Medul Mendoza
    7. Marvin Cato
    8. Reymark Togno
    9. Lim Jing Ren
    10. Rindell Mabunga
    11. Jeffrey Robles
    12. Sumet Ketsri
    13. Isaiah James de Dios Maling
    14. Lilanie Monique Torilla
    15. Lenard Guillermo
    16. Jacob Sabido
    17. Joem Canciller
    18. Gluttony
    19. Andrew Chiu
    20. Roenz Joshlee Timbol
    21. Mark Alvero
    22. Randy Orton
    23. Willie Revillame Wowowin
 
46. Problem: 7964 , proposed by Amirul Faiz Abdul Muthalib, Tip: Key Fact(s): 7695
46 is the number of chromosomes all human beings have in every cell of their body.
What is the smallest positive integer $n \neq 2017$ such that the fraction $$\frac{n-2017}{20n+17}$$ is NOT in its simplest form (reducible fraction)? Ah Math

  • Correct answers have been submitted by:
    1. Nixon Balandra
    2. Marvin Cato
    3. Sumet Ketsri
    4. Rindell Mabunga
    5. Kurara Chibana
    6. Russel J. Galanido
    7. Lim Jing Ren
    8. Caed Mark Medul Mendoza
    9. Andrew Chiu
    10. Isaiah James de Dios Maling
    11. Jeffrey Robles
    12. Roenz Joshlee Timbol
    13. Randy Orton
    14. Willie Revillame Wowowin
 
47. Problem: 76AC , proposed by Amirul Faiz Abdul Muthalib
47 is the largest number of cubes that cannot tile a cube.
Four consecutive integers are greater than $2017$. The smallest is divisible by $5$, the second is divisible by $7$, the third is divisible by $9$, and the largest is divisible by $11$. Find the sum of the smallest such consecutive integers. Ah Math

  • Correct answers have been submitted by:
    1. Isaiah James de Dios Maling
    2. Rindell Mabunga
    3. Kurara Chibana
    4. Russel J. Galanido
    5. Lim Jing Ren
    6. Caed Mark Medul Mendoza
    7. Lilanie Monique Torilla
    8. Marvin Cato
    9. Sumet Ketsri
    10. Jeffrey Robles
    11. Mark Alvero
    12. Roenz Joshlee Timbol
    13. Randy Orton
    14. Willie Revillame Wowowin
 
48. Problem: D256 , proposed by Ahmet Arduc
1971 is the birth year of A. Arduc.
The factorial base of numeration is defined as $a_1+a_2⋅2!+a_3⋅3!+...+a_n⋅n!$ where $a_1,a_2,...,a_n$ are integer coefficients such that $0≤a_k≤k$. Thus, 1971 can be written in factorial base of numeration as $$1+1⋅2!+0⋅3!+2⋅4!+4⋅5!+2⋅6!$$ where the sum of the coefficients is 10. What is the sum of all coefficients used in factorial base of numeration to write all numbers from 1 to 2017? Ah Math

  • Correct answers have been submitted by:
    1. Kurara Chibana
    2. Russel J. Galanido
    3. Amirul Faiz Abdul Muthalib
    4. Marvin Cato
    5. Kimi No Nawa
    6. Caed Mark Medul Mendoza
    7. Rindell Mabunga
    8. Lilanie Monique Torilla
    9. Sumet Ketsri
 
49. Problem: 8D49 , proposed by Ahmet Arduc, Tip: Key Fact(s): 7695
49 is the smallest number with exactly 8 representations as a sum of three distinct primes.
Given $$A=\frac{1}{2017}+\frac{2}{2017^2}+\frac{3}{2017^3}+...$$ whose $n$ th term is $\large{\frac{n}{2017^n}}$. If $A$ is written in its simplest form as $\large{\frac{a}{b}}$, what is the sum of $a$ and $b$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Isaiah James de Dios Maling
    2. Amirul Faiz Abdul Muthalib
    3. Kurara Chibana
    4. Russel J. Galanido
    5. Marvin Cato
    6. Kimi No Nawa
    7. Caed Mark Medul Mendoza
    8. Sumet Ketsri
    9. Rindell Mabunga
    10. Joem Canciller
    11. Daniel James Molina
    12. Lilanie Monique Torilla
    13. Jacob Sabido
    14. Andrew Chiu
    15. Nixon Balandra
    16. Jeffrey Robles
    17. Roenz Joshlee Timbol
    18. Randy Orton
    19. Willie Revillame Wowowin
 
50. Problem: 7E39 , proposed by Amirul Faiz Abdul Muthalib
50 is the smallest number that can be written as the sum of 2 squares in 2 distinct ways.
Given two sequences ${{a}_{n}}$ and ${{b}_{n}}$ with initial terms $a_1$ and $b_1$ such that ${{a}_{1}}={{b}_{1}}=2017$,\[{{a}_{2}}=2!\,+0!\,+1!\,+7!=5044,\text{ }{{a}_{3}}=5!\,+0!\,+4!\,+4!=169,\,\,\ldots \] which every term of ${{a}_{n}}$is the sum of the factorial of the digits of the preceding term, \[{{b}_{2}}={{2}^{2}}+{{0}^{2}}+{{1}^{2}}+{{7}^{2}}=54,\text{ }{{b}_{3}}={{5}^{2}}+{{4}^{2}}=41,\text{ }{{b}_{4}}={{4}^{2}}+{{1}^{2}}=17,\ldots \]which every term of ${{b}_{n}}$ is the sum of the squares of the digits of the preceding term. What is the value of ${{a}_{2017}}+{{b}_{2017}}$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Kurara Chibana
    2. Russel J. Galanido
    3. Caed Mark Medul Mendoza
    4. Lilanie Monique Torilla
    5. Marvin Cato
    6. Sumet Ketsri
    7. Andrew Chiu
    8. Nixon Balandra
    9. Isaiah James de Dios Maling
    10. Rindell Mabunga
    11. Jeffrey Robles
    12. Mark Alvero
    13. Randy Orton
    14. Willie Revillame Wowowin
 
51. Problem: 4E84 , proposed by Ahmet Arduc
51 is the 6th Motzkin number.
The 51 stars of the US flag are numbered from 1 to 51, from top right corner to lower left corner. 13 of them are picked at random. Among those selected, if the probability that the third smallest is numbered as 7 is an irreducible fraction $\large{\frac{a}{b}}$, what is the sum of $a$ and $b$ $?$ Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Sumet Ketsri
    3. Kurara Chibana
    4. Russel J. Galanido
    5. Kimi No Nawa
    6. Caed Mark Medul Mendoza
    7. Isaiah James de Dios Maling
    8. Jeffrey Robles
    9. Rindell Mabunga
 
52. Problem: EE37 , proposed by Amirul Faiz Abdul Muthalib
52 is the 5th Bell number.
How many ways are there to choose 4 distinct integers, $\{a,\,b,\,c,\,d\}$, from the set $N=\{1,\,2,\,3,\,...\,, 2016,\,2017\}$ such that $\{a,\,b,\,c,\,d\}$ form an increasing geometric sequence with a common ratio of positive integer? Ah Math

  • Correct answers have been submitted by:
    1. Sumet Ketsri
    2. Kurara Chibana
    3. Russel J. Galanido
    4. Kimi No Nawa
    5. Caed Mark Medul Mendoza
    6. Isaiah James de Dios Maling
    7. Lilanie Monique Torilla
    8. Jeffrey Robles
    9. Roenz Joshlee Timbol
    10. Mark Alvero
    11. Rindell Mabunga
    12. Radu Bogo
    13. Reymark Togno
 
53. Problem: 2D73 , proposed by Ahmet Arduc
64 is the smallest number with 7 divisors.
Let $S(n)$ and $P(n)$ denote the sum and the product, respectively, of the digits of the integer $n$. For example, $S(64)=6+4=10$ and $P(64)=6 \cdot 4=24$. Let $N$ be the sum of $S(N)$ and $P(N)$. What is the sum of all two-digit $N$ numbers? Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Isaiah James de Dios Maling
    3. Kimi No Nawa
    4. Lilanie Monique Torilla
    5. Caed Mark Medul Mendoza
    6. Kurara Chibana
    7. Russel J. Galanido
    8. Jeffrey Robles
    9. Reymark Togno
    10. Rindell Mabunga
    11. Roenz Joshlee Timbol
 
54. Problem: E584 , proposed by Amirul Faiz Abdul Muthalib
54 is the smallest number that can be written as the sum of 3 squares in 3 ways.
A polynomial $P(x)$ of degree $2016$ satisfies $$P(0)=0,\,\,P(1)=\frac{1}{2},\,\,P(2)=\frac{2}{3},\,\,P(3)=\frac{3}{4},\,\,\ldots ,\,\,P(2016)=\frac{2016}{2017} .$$ If $P(2017)$ form an irreducible fraction of $\large{\frac{a}{b}}$, what is $a+b$? Ah Math

 
55. Problem: 86C7 , proposed by Ahmet Arduc
55 is the largest triangular number in the Fibonacci sequence.
Consider the sequence of numbers$$1,\,2,\,3,\,5,\,8,\,3,\,1,\,...$$ For $n>2$, the $n$th term of the sequence is the units digit of the sum of the two previous terms. What is the sum of the first 2017 terms? Ah Math

  • Correct answers have been submitted by:
    1. Amirul Faiz Abdul Muthalib
    2. Isaiah James de Dios Maling
    3. Kurara Chibana
    4. Russel J. Galanido
    5. Caed Mark Medul Mendoza
    6. Jeffrey Robles
    7. James Ericson
    8. Reymark Togno
    9. Sumet Ketsri
    10. Nixon Balandra
    11. Jacob Sabido
    12. Stefano Ongari
    13. Randy Orton
    14. Willie Revillame Wowowin
    15. Rindell Mabunga
 
56. Problem: DAA3 , proposed by Ahmet Arduc
co-writer: Mehmet Emin Arduc.
After a certain dilation, if point $(86,286)$ maps onto point $(103,343)$, point $(106,126)$ maps onto point $(127,151)$, and point $(a,b)$ maps onto point $(2017,2017)$, what is the sum of $a$ and $b$ $?$ Ah Math

 
57. Problem: 7B63 , proposed by Ahmet Arduc
57 because this it the 57th problem :-)
The sum of 57 consecutive positive integers is a perfect square. What is the smallest possible value of this sum? Ah Math

  • Correct answers have been submitted by:
    1. Caed Mark Medul Mendoza
    2. Kimi No Nawa
    3. Amirul Faiz Abdul Muthalib
    4. James Ericson
    5. Jacob Sabido
    6. Roenz Joshlee Timbol
    7. Kurara Chibana
    8. Russel J. Galanido
    9. Sumet Ketsri
    10. Jeffrey Robles
    11. Dan Lang
    12. Rindell Mabunga
    13. Reymark Togno
    14. Randy Orton
    15. Radu Bogo
    16. Willie Revillame Wowowin
    17. Lilanie Monique Torilla
 
58. Problem: 5484 , proposed by Ahmet Arduc
18 is the only number that is twice the sum of its digits.
$$A=2!\cdot4!\cdot6!\cdot8!\cdot10!\cdot12!\cdot14!\cdot16!\cdot18!$$ How many perfect squares are divisors of $A$? Ah Math

  • Correct answers have been submitted by:
    1. Jeffrey Robles
    2. Ikemen
    3. Kimi No Nawa
    4. Caed Mark Medul Mendoza
    5. Amirul Faiz Abdul Muthalib
    6. Kurara Chibana
    7. Russel J. Galanido
    8. Rindell Mabunga
    9. Stefano Ongari
    10. Lilanie Monique Torilla
    11. Randy Orton
    12. Willie Revillame Wowowin
 
59. Problem: B18D , proposed by Amirul Faiz Abdul Muthalib
Watch first S2E2 of NUMB3RS (the television crime drama): Better or Worse.
The irreducible fractions between $0$ and $1$ are listed in ascending order, with denominators that are at most $2017$. What is the sum of $a$, $b$, $c$, and $d$, if $\large{\frac{a}{b}}$ and $\large{\frac{c}{d}}$ are two adjacent fractions of $\large{\frac{17}{20}}$ $?$ Ah Math

 
60. Problem: B57E , proposed by Ahmet Arduc
A Platonic Solid: Cube.
Numbers from the set $\{1, 289, 577, 865, 1153, 1441, 1729, 2017\}$ are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same. What is this common sum? Ah Math

  • Correct answers have been submitted by:
    1. Kurara Chibana
    2. Russel J. Galanido
    3. Randy Orton
    4. Sumet Ketsri
    5. Willie Revillame Wowowin
    6. Kimi No Nawa
    7. Caed Mark Medul Mendoza
    8. Lilanie Monique Torilla
    9. Rindell Mabunga
    10. Jeffrey Robles
 
61. Problem: B375 , proposed by Ahmet Arduc
61 is the smallest prime whose reversal (16) is a square.
$$A=1\cdot2!\cdot3!\,\cdot \,...\, \cdot\,2017!$$ What is the sum of the units and the tens digit of $A$ $?$ Ah Math

 
62. Problem: A3BD , proposed by Ahmet Arduc
62 is the smallest number that can be written as the sum of 3 distinct squares in 2 ways.
The first term of a sequence is 2017. Each succeeding term is the sum of the squares of the digits of the previous term. What is the 2017th term of the sequence? Ah Math

  • Correct answers have been submitted by:
    1. Randy Orton
    2. Willie Revillame Wowowin
    3. Kurara Chibana
    4. Russel J. Galanido
    5. Caed Mark Medul Mendoza
    6. Lilanie Monique Torilla
    7. Roenz Joshlee Timbol
    8. Jeffrey Robles
 
63. Problem: 513D , proposed by Ahmet Arduc
63 is the number of partially ordered sets of 5 elements.
$$3^{280} \lt n^{140} \lt (k\cdot n)^{70}$$ If there are 2017 positive integers $n$ that satisfies the given inequality, what is the positive value of $k \,?$ Ah Math

  • Correct answers have been submitted by:
    1. Randy Orton
    2. Willie Revillame Wowowin
    3. Kurara Chibana
    4. Russel J. Galanido
    5. Kimi No Nawa
    6. Caed Mark Medul Mendoza
    7. Lilanie Monique Torilla
    8. Jeffrey Robles
 
64. Problem: D8E1 , proposed by Ahmet Arduc, Tip: Key Fact(s): B13A
64 is the smallest number with 7 divisors.
A lattice point is a point in the plane with integer coordinates. How many lattice points are on the line segment whose endpoints are $(45, 64)$ and $(1971, 2017)$, both ends excluded? Ah Math

 
65. Problem: 89E9 , proposed by Ahmet Arduc
65 is the lowest integer that becomes square if its reverse is either added to or subtracted from it.
A 65×65×65 woden cube is formed by gluing together $65^3$ unit cubes. What is the least number of unit cubes that cannot be seen from a single point? Ah Math

 
66. Problem: 792C , proposed by Amirul Faiz Abdul Muthalib
66 is a triangular palindromic number.
Given that $z$ is a complex number such that $\large{z+\frac{1}{z}}=\normalsize{2\cos17}^{\circ}$. Find the least integer that is greater than $${\left( {{z}^{2017}}+\frac{1}{{{z}^{2017}}} \right)}^{-1}$$ Ah Math

 
67. Problem: 1D15 , proposed by Ahmet Arduc
67 is the smallest number which is both palindromic in base 5 and in base 6.
A two-digit number sequence is as follows: $$13, 92, 78, 12, 43, 72, a, b, c, ...$$ What is the sum of $a$, $b$, and $c$ of this sequence? Ah Math

 
68. Problem: BB2C , proposed by Amirul Faiz Abdul Muthalib
68 is the smallest composite number that becomes prime by turning it upside down.
Amirul and Ahmet play a game. Each player, in turn, has to name a natural number that is less than but at least half the previous number. The player who names the number $1$ loses. If Amirul starts by naming $2017$, what is the next number that Ahmet should choose to ensure that he will win at the end? Ah Math

 
69. Problem: C294 , proposed by Ahmet Arduc
69 is a value of n where n² and n³ together contain each digit once.
A bag contains 69 marbles, numbered with the first 69 prime numbers. 5 marbles are drawn simultaneously at random. Among those selected, if the probability that the sum of the numbers on the marbles drawn is even is an irreducible fraction $\large{\frac{a}{b}}$, what is the sum of $a$ and $b$ $?$ Ah Math

 
70. Problem: D8E5 , proposed by Ahmet Arduc, Tip: Key Fact(s): C181
70 is the smallest weird number.
Find the least positive integer that has exactly 70 positive integer divisors. Ah Math

 

☆★☆★☆★  Newest Problem!  ★☆★☆★☆

71. Problem: 99E4 , proposed by Ahmet Arduc
71 divides the sum of the primes less than it.
The four points $A(2, 2)$, $B(10, 1)$, $C(2017, t)$, and $D(1, 7)$ lie in the coordinate plane. If $P(7, 3)$ is the point to get the minimum possible value of $PA+PB+PC+PD$ over all points on the plane, what is the value of $t$ $?$ Ah Math

 
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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.

Order Score # of Correct Answers Names Badges Country
FSSF
1.076.08
55Sumet Ketsri556 ThailandThailand
2.076.06
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61Amirul Faiz Abdul Muthalib80 MalaysiaMalaysia
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10.061.77
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11.053.20
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12.052.65
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26Joem Canciller10 PhilippinesPhilippines
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14John Albert A. Reyes06 PhilippinesPhilippines
30.018.50
17Nheil Ignacio08 PhilippinesPhilippines
31.017.74
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38.012.68
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40.011.27
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16Stefano Ongari00 ItalyItaly
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Key Fact 7446
The product of a rational number and an irrational number is irrational. Ah Math

Key Fact 7695
For a fraction to be in lowest terms (or, to be written in its simplest form), its numerator and denominator must be relatively prime. Ah Math

Key Fact ABAD
The square of any even integer is of form $4k$. Ah Math

Key Fact BAB3
The square of any odd integer is of form $4k+1$. Ah Math

Key Fact 988C
The product of four consecutive natural numbers is never a perfect square. Ah Math

Key Fact 9A34
$$1001=7\cdot11\cdot13$$ Ah Math

Key Fact B664
$$n\cdot n!=(n+1)!-n!$$ Ah Math

Key Fact 969B
$$\frac{1}{n\cdot(n+1)}=\frac{1}{n}-\frac{1}{n+1}$$ Ah Math

Key Fact CE81
$$\frac{1}{n \cdot (n+m)}=\frac{1}{m} \left( \frac{1}{n}-\frac{1}{n+m} \right)$$ Ah Math

Key Fact B945
$$\frac{1}{n(n+1)(n+2)}=\frac{1}{2}\cdot \left[ \frac{1}{n(n+1)} - \frac{1}{(n+1)(n+2)} \right]$$ Ah Math

Key Fact BCC8
$$\frac{n}{(n+1)!}=\frac{1}{n!}-\frac{1}{(n+1)!}$$ Ah Math

Key Fact 965A
$$n^4+n^2+1=(n^2+1-n)\cdot(n^2+1+n)$$ Ah Math

Key Fact E856
$$(n+1)^2-(n+1)+1=n^2+n+1$$ Ah Math

Key Fact 7C45
$\small{\textbf{Sophie-Germain Identity}}$: $$\begin{align}a^4+4b^4&\cssId{Step1}{=\left[(a+b)^2+b^2\right]\left[(a-b)^2+b^2\right]}\\&\cssId{Step1}{=(a^2+2ab+2b^2)(a^2-2ab+2b^2)} \end{align}$$ Ah Math

Key Fact EA1C
$$x^4+y^4+z^4=(x^2+y^2+z^2)^2-2(x^2y^2+y^2z^2+x^2z^2)$$ Ah Math

Key Fact 3E17
For odd $n \in N$, $$a^n+b^n=(a+b)(a^{n-1}-a^{n-2} \cdot b \,+\,...\,-\,a \cdot b^{n-2}+b^{n-1})$$ Ah Math

Key Fact 2545
For all $n \in N$, $$a^n-b^n=(a-b)(a^{n-1}+a^{n-2} \cdot b \,+\,...\,+\,a \cdot b^{n-2}+b^{n-1})$$ Ah Math

Key Fact A376
For $a=k\cdot (2k+1)$ where $k \in N$,$$a^2+(a+1)^2+⋯+(a+k)^2\\=(a+k+1)^2+(a+k+2)^2+⋯+(a+2k)^2$$ Ah Math

Key Fact C181
If $p$ is a prime number, then the prime power $p^a$ has $a+1$ divisors. Ah Math

Key Fact 8A33
The square of any odd integer leaves remainder 1 upon division by 8. Ah Math

Key Fact 7B55
When $n$ is a positive even integer,$$n⋅(n+4)⋅(n+8)⋅(n+12)$$is divisible by 8. Ah Math

Key Fact 8C41
$n^3-n$ is always divisible by 6, where $n \in Z$. Ah Math

Key Fact 8632
The product of any $n$ consecutive integer is always divisible by $n!$ Ah Math

Key Fact EADA
If $n$ is a positive integer,$$(n+1)\cdot(n+2)⋅…⋅(2n)$$is divisible by $2^n$. Ah Math

Key Fact A4A7
The binomial expansion of $(x+y)^n$ has $n+1$ terms. Ah Math

Key Fact 3845
The binomial expansion of $$(a_1+a_2+⋯+a_{r-1}+a_r )^n$$has $\large {n+r-1 \choose r-1}$ terms. Ah Math

Key Fact D8CD
$$1+2+3\,+\,...\,+\,n=\frac{n(n+1)}{2}$$ Ah Math

Key Fact DEA5
$$1^2+2^2+3^2\,+\,...\,+\,n^2=\frac{n(n+1)(2n+1)}{6}$$ Ah Math

Key Fact 7B38
$$1^3+2^3+3^3+...+\,n^3=\left[\frac{n(n+1)}{2}\right]^2$$ Ah Math

Key Fact 2EBB
$$1^4+2^4+3^4+...+\,n^4=\frac{pst}{30}$$ where $p=n(n+1)$, $s=2n+1$, and $t=3p-1$. Ah Math

Key Fact 89DD
$$\sum_{k=1}^n k \cdot (k+1) \cdot (k+2) = \frac{n\cdot(n+1)\cdot(n+2)\cdot(n+3)}{4}$$ Ah Math

Key Fact ECD9
There are $$\frac{n\cdot(n+1)\cdot(2n+1)}{6}$$squares on an $n\times n$ chessboard. Ah Math

Key Fact A86B
The $\small{\textbf{Arithmetic Mean}}$ ($\small{\textbf{AM}}$) of positive real numbers $x_1, x_2, ...,x_n$ is defined as$$\frac{x_1 + x_2 + ... + x_n}{n}$$ Ah Math

Key Fact B65C
The $\small{\textbf{Geometric Mean}}$ ($\small{\textbf{GM}}$) of positive real numbers $x_1, x_2, ...,x_n$ is defined as$$\root n \of {x_1 \cdot x_2 \cdot ...\cdot x_n}$$ Ah Math

Key Fact D477
For any set of positive real numbers $x_1,\ldots,x_n$, the arithmetic mean is greater than or equal to the geometric mean. That is,$$\frac{x_1 + x_2 + ... + x_n}{n}\ge\root n \of {x_1 \cdot x_2 \cdot ...\cdot x_n}$$ Ah Math

Key Fact DDC5
The $\small{\textbf{Harmonic Mean}}$ ($\small{\textbf{HM}}$) of positive real numbers $x_1, x_2, ...,x_n$ is defined to be$$\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}$$ Ah Math

Key Fact 29D9
For any set of positive real numbers $x_1,\ldots,x_n$, the arithmetic mean is greater than or equal to the harmonic mean. That is,$$\frac{x_1 + x_2 + ... + x_n}{n}\ge\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}$$ Ah Math

Key Fact 5375
For non-zero real numbers $a$ and $b$,$$\frac{a}{b}+\frac{b}{a}\ge2$$ Ah Math

Key Fact 1E7C
For real numbers $a$ and $b$, $$a^2+b^2+1 \ge ab+a+b$$ Ah Math

Key Fact 3981
For real numbers $a$ and $b$, $$a^4+b^4+8 \ge 8ab$$ Ah Math

Key Fact 1EB9
For positive real numbers $a$, $b$, and $c$, $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\le\frac{a^2+b^2+c^2}{a\cdot b\cdot c}$$ Ah Math

Key Fact D7B8
For positive real numbers $a$, $b$, and $c$, $$\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge3$$. Ah Math

Key Fact 2483
For real numbers $a,b,c \ge 0$, $$(a+b)\cdot(a+c)\cdot(b+c) \ge 8abc$$ Ah Math

Key Fact 6C13
For real numbers $a,b,c \ge 0$, $$(a^2+1)\cdot(b^2+1)\cdot(c^2+1) \ge 8abc$$ Ah Math

Key Fact 7185
For real numbers $a,b,c\ge0$, $$ab+ac+bc\ge a \cdot \sqrt{bc}+b \cdot \sqrt{ac}+c \cdot \sqrt{ab}$$ Ah Math

Key Fact 8C62
For positive real numbers $a$, $b$, $c$, and $d$, $$(a+b+c+d)\cdot \left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d} \right)\ge16$$ Ah Math

Key Fact 913D
$$(1+x)^n\ge(1+n\cdot x)$$ Ah Math

Key Fact ADBA
$\small{\textbf{Cauchy–Schwarz Inequality}}:\\[0pt]$ $\text{For all sequences of real numbers $a_i$ and $b_i$, we have}$ $$\left(\sum_{i=1}^n a_i^2\right)\cdot\left(\sum_{i=1}^n b_i^2\right)\ge\left(\sum_{i=1}^n a_i\cdot b_i\right)^2$$ Ah Math

Key Fact 2169
$\small{\textbf{ Chebyshev Inequality}}:\\[5pt]\text{ Let }x_1, x_2,..., x_n \text{ and } y_1, y_2,..., y_n \text{ be two sequences of real }\\ \text{ numbers, such that } x_1 \le x_2 \le \cdots \le x_n \text{ and } y_1 \le y_2 \le \cdots \le y_n. \\ \text{ Then, }$$$\frac{(x_1+x_2+...+x_n)(y_1+y_2+...+y_n)}{n} \le x_1y_1+x_2y_2+...+x_ny_n$$ Ah Math

Key Fact E1B9
Let $y=k$ be any line which intersects $y=ax^2+bx+c$ at two points, say $P$ and $Q$, where $a, b, c, k \in R$ and $a \neq 0$. Then the abscissa of the midpoint of the line segment $PQ$ is the abscissa of the vertex of the parabola. Ah Math

Key Fact 72A4
$\small{\textbf{De Moivre's Formula}}:$ For any angle $\alpha$ and for any integer $n$, $$(\text{cos } \alpha + i\cdot \text{sin } \alpha)^n=\text{cos } n\alpha + i\cdot \text{sin } n\alpha$$ Ah Math

Key Fact 5DB3
$\small{\textbf{Fibonacci Numbers}}:\\[0pt]\text{Sequence defined recursively by } F_1=F_2=1 \text{ and } F_{n+2}=F_{n+1}+F_n \\ \text{for all } n \in N.$ Ah Math

Key Fact 47EB
A finite series is given by all the terms of a finite sequence, added together. Ah Math

Key Fact 13D3
An infinite series is given by all the terms of an infinite sequence, added together. Ah Math

Key Fact EAA4
The $n$th partial sum of a series is the sum of the first $n$ terms. Ah Math

Key Fact 3332
The sequence of partial sums of a series sometimes tends to a real limit. If this happens, we say that this limit is the sum of the series. Ah Math

Key Fact 2B69
The sequence of partial sums of a series sometimes tends to a real limit. If this does not happen, we say that the series has no sum. Ah Math

Key Fact C62B
A series can have a sum only if the individual terms tend to zero. But there are some series (with individual terms tending to zero) that do not have sums. Ah Math

Key Fact 1529
The sum of an infinite series of the form $$a_1+a_1\cdot r+a_1\cdot r^2+a_1\cdot r^3+...$$ is $\large{\frac{a_1}{1-r}}$ where $\left| r \right| < 1$. Ah Math

Key Fact E6E7
Relative error = error / measurement Ah Math

Key Fact 8B56
The bisector of an angle of the triangle divides the opposite side into segments proportional to the other two sides. Ah Math

Key Fact B4C3
The sum of the exterior angles of any (convex) polygon is a constant, namely two straight angles (360$^{\circ}$). Ah Math

Key Fact C4CC
Of all triangles inscribable in a semi-circle, with the diameter as base, the one with the greatest area is the one with the largest altitude (the radius); that is, isosceles triangle. Ah Math

Key Fact 8146
Two equal circles in a plane cannot have only one common tangent. Ah Math

Key Fact B13A
The number of lattice points on the segment from the origin to $(a,b)$ is one more than the greatest common factor of $a$ and $b$. Ah Math

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.

Please feel free to send your general comments to challenging-problems@ahmath.com.


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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Solutions to all 19 Challenging Math Problems is ready!
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