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Pandigital ABCs (Posted on 2009-12-28) Difficulty: 3 of 5
(A,B,C) is a 'pandigital' set of positive integers where the concatenated A|B|C is comprised of all, and only, the ten decimal digits (0 to 9) with no repeated digits. (In the following, except where the base number has a radix, all integers are in base 10.) How many of these 'pandigital' sets exist for
  • AB = C [A in base B equals C]
  • AB = C [A to the power of B equals C]
Provide a separate value for each specification.

  Submitted by Dej Mar    
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Solution: (Hide)
For AB = C : 48
  1. (34105,    7,  8629)
  2. (13074,    8,  5692)
  3. (21547,    8, 99063)
  4. ( 5730,   12,  9684)
  5. ( 3672,   14,  9508)
  6. (  865,   39, 12407)
  7. (  568,   49, 12307)
  8. (  436,   52, 10978)
  9. (  706,   52, 18934)
  10. (  682,   54, 17930)
  11. (  701,   59, 24368)
  12. (  502,   63, 19847)
  13. (  802,   67, 35914)
  14. (  510,   69, 23874)
  15. (  360,   72, 15984)
  16. (  675,   83, 41920)
  17. (  304,   85, 21679)
  18. (  203,   86, 14795)
  19. (  270,   86, 15394)
  20. (  279,   86, 15403)
  21. (  205,   96, 18437)
  22. (  835,   96, 74021)
  23. (  340,   97, 28615)
  24. (   85, 1204,  9637)
  25. (   47, 1269,  5083)
  26. (   46, 1273,  5098)
  27. (   58, 1279,  6403)
  28. (   65, 1304,  7829)
  29. (   67, 1342,  8059)
  30. (   75, 1403,  9826)
  31. (   40, 1738,  6952)
  32. (   28, 1749,  3506)
  33. (   39, 1806,  5427)
  34. (   45, 1826,  7309)
  35. (   40, 1963,  7852)
  36. (   37, 2059,  6184)
  37. (   39, 2157,  6480)
  38. (   34, 2605,  7819)
  39. (   25, 3407,  6819)
  40. (   28, 3471,  6950)
  41. (   28, 3519,  7046)
  42. (   28, 3549,  7106)
  43. (   25, 3698,  7401)
  44. (   25, 4067,  8139)
  45. (   25, 4079,  8163)
  46. (   25, 4307,  8619)
  47. (   28, 4671,  9350)
  48. (   28, 4761,  9530)

For AB = C : 0, as all integers is given to be greater than zero. If B were permitted to be 0 (as was my initial intent to allow), the value would be 40320 (8! permutations of the digits 2 through 9 for A, with B and C being 0 and 1, respectively).

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutioncomputer solution to part 1Charlie2009-12-29 14:48:26
re(2): Part 2: Trivial (?) solutionsSteve Herman2009-12-29 10:24:23
SolutionPart 2 solutionJustin2009-12-28 19:53:52
re: Part 2: Trivial (?) solutionsJustin2009-12-28 19:33:34
Hints/TipsPart 2: Trivial (?) solutionsSteve Herman2009-12-28 19:20:33
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