Statistics

Problem Statement for "Yllion"

Problem Statement

The -yllion notation is an alternate notation for powers of 10 designed by Donald Knuth. The main feature of this notation is that the grouping of digits is exponential, not linear. That is, each new name is used to double the number of digits. Equivalently, each new name represents a power of ten whose exponent is twice the previous one. Below we explain this in more detail.

Knuth's names for the powers of 10 are constructed as follows:

  • As usual, 10^0 is called "one" and 10^1 is called "ten".
  • The next two powers of ten are the hundreds: 10^2 is "one hundred" and 10^3 is "ten hundred".
  • The following four powers are the myriads. That is, 10^4 is "one myriad", and the others follow logically: 10^5 is "ten myriad", 10^6 is "one hundred myriad", and 10^7 is "ten hundred myriad".
  • The eight powers that follow are the myllions: 10^8 is "one myllion", 10^9 is "ten myllion", ..., and 10^15 is "ten hundred myriad myllion".
  • ...

The next names used after "myllion" are the following ones: "byllion", "tryllion", "quadryllion", "quintyllion", "sextyllion", "septyllion", "octyllion", "nonyllion", and "decyllion". Each is appended after all the previous ones, and the value of each is the square of the previous one. That is, "one byllion" is 10^16, "one tryllion" is 10^32, "one quadryllion" is 10^64, and so on.

You are given the Strings a and b that each describe a valid power of 10 in Knuth's notation. Return a String containing Knuth's name for their product.

Definition

Class:
Yllion
Method:
getPower
Parameters:
String, String
Returns:
String
Method signature:
String getPower(String a, String b)
(be sure your method is public)

Constraints

  • a and b will be valid powers of 10 in Knuth's notation.
  • a and b will each be strictly smaller than "one decyllion".

Examples

  1. "one"

    "one"

    Returns: "one"

    One times one is one.

  2. "one"

    "ten"

    Returns: "ten"

  3. "one hundred"

    "one hundred"

    Returns: "one myriad"

    Remember that you have to express the answer in Knuth's notation as well. Our 10,000 (ten thousand) is called "one myriad".

  4. "ten hundred"

    "one hundred"

    Returns: "ten myriad"

  5. "ten hundred myriad myllion"

    "one hundred myllion tryllion"

    Returns: "ten myllion byllion tryllion"

  6. "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    "ten"

    Returns: "one decyllion"

    This a is the largest possible number that can appear in the input.

  7. "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "one hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion decyllion"

  8. "one myriad myllion quadryllion sextyllion septyllion nonyllion"

    "one myriad byllion sextyllion septyllion nonyllion"

    Returns: "one tryllion quadryllion septyllion octyllion decyllion"

  9. "ten hundred myriad myllion tryllion sextyllion septyllion nonyllion"

    "one hundred myriad tryllion septyllion nonyllion"

    Returns: "ten myriad byllion quadryllion sextyllion octyllion decyllion"

  10. "one hundred myllion byllion quintyllion septyllion"

    "one hundred byllion quadryllion sextyllion septyllion nonyllion"

    Returns: "one myriad myllion tryllion quadryllion quintyllion sextyllion octyllion nonyllion"

  11. "one myriad byllion tryllion septyllion octyllion nonyllion"

    "one tryllion quintyllion septyllion"

    Returns: "one myriad byllion quadryllion quintyllion decyllion"

  12. "one tryllion quadryllion sextyllion septyllion octyllion"

    "one hundred myriad byllion tryllion quadryllion quintyllion octyllion"

    Returns: "one hundred myriad byllion quadryllion octyllion nonyllion"

  13. "one hundred myriad byllion quadryllion sextyllion septyllion octyllion nonyllion"

    "ten hundred myriad quadryllion"

    Returns: "ten myriad myllion byllion quintyllion sextyllion septyllion octyllion nonyllion"

  14. "one hundred myllion byllion tryllion quintyllion septyllion nonyllion"

    "one hundred myriad myllion byllion tryllion quadryllion quintyllion septyllion octyllion"

    Returns: "one myllion byllion tryllion quintyllion sextyllion decyllion"

  15. "one myriad quadryllion septyllion"

    "ten myriad myllion quadryllion quintyllion"

    Returns: "ten byllion sextyllion septyllion"

  16. "ten hundred myllion quintyllion"

    "ten hundred tryllion quintyllion sextyllion septyllion octyllion"

    Returns: "one hundred myriad myllion tryllion nonyllion"

  17. "ten myriad quadryllion"

    "ten myriad byllion tryllion quintyllion octyllion nonyllion"

    Returns: "one hundred myllion byllion tryllion quadryllion quintyllion octyllion nonyllion"

  18. "one hundred septyllion nonyllion"

    "one myllion quadryllion quintyllion septyllion nonyllion"

    Returns: "one hundred myllion quadryllion quintyllion octyllion decyllion"

  19. "one hundred myriad myllion quintyllion sextyllion septyllion nonyllion"

    "one myriad myllion byllion tryllion quadryllion septyllion"

    Returns: "one hundred myllion septyllion octyllion nonyllion"

  20. "one hundred myllion byllion quintyllion sextyllion"

    "one myriad myllion byllion tryllion quadryllion quintyllion septyllion"

    Returns: "one hundred myriad byllion quintyllion octyllion"

  21. "ten byllion tryllion quintyllion octyllion"

    "one sextyllion nonyllion"

    Returns: "ten byllion tryllion quintyllion sextyllion octyllion nonyllion"

  22. "ten hundred myllion tryllion sextyllion septyllion nonyllion"

    "one myriad byllion quadryllion sextyllion septyllion octyllion"

    Returns: "ten hundred myriad myllion byllion tryllion quadryllion septyllion decyllion"

  23. "one myllion tryllion sextyllion septyllion"

    "one hundred myllion septyllion"

    Returns: "one hundred byllion tryllion sextyllion octyllion"

  24. "one hundred byllion tryllion quintyllion sextyllion nonyllion"

    "one myriad myllion tryllion quadryllion quintyllion octyllion"

    Returns: "one hundred myriad myllion byllion quintyllion septyllion octyllion nonyllion"

  25. "ten myllion tryllion sextyllion nonyllion"

    "one hundred myriad byllion quintyllion nonyllion"

    Returns: "ten hundred myriad myllion byllion tryllion quintyllion sextyllion decyllion"

  26. "one myllion quadryllion quintyllion sextyllion septyllion octyllion"

    "ten hundred myriad myllion byllion quadryllion sextyllion septyllion octyllion nonyllion"

    Returns: "ten hundred myriad tryllion sextyllion septyllion octyllion decyllion"

  27. "one myriad myllion tryllion sextyllion octyllion"

    "ten myriad myllion byllion tryllion quintyllion sextyllion septyllion octyllion"

    Returns: "ten myllion tryllion quadryllion quintyllion octyllion nonyllion"

  28. "ten hundred myriad myllion byllion quintyllion sextyllion septyllion octyllion nonyllion"

    "ten hundred myllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "one hundred myllion quintyllion sextyllion septyllion octyllion nonyllion decyllion"

  29. "one byllion sextyllion"

    "ten hundred myllion byllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "ten hundred myllion tryllion quadryllion quintyllion decyllion"

  30. "ten hundred myriad byllion quadryllion quintyllion sextyllion nonyllion"

    "one myllion"

    Returns: "ten hundred myriad myllion byllion quadryllion quintyllion sextyllion nonyllion"

  31. "one myriad septyllion"

    "one myriad myllion septyllion octyllion"

    Returns: "one byllion nonyllion"

  32. "ten"

    "one hundred myriad byllion tryllion quadryllion quintyllion sextyllion nonyllion"

    Returns: "ten hundred myriad byllion tryllion quadryllion quintyllion sextyllion nonyllion"

  33. "ten hundred byllion tryllion quintyllion nonyllion"

    "one hundred quadryllion septyllion octyllion nonyllion"

    Returns: "ten myriad byllion tryllion quadryllion quintyllion septyllion octyllion decyllion"

  34. "ten myriad tryllion quadryllion septyllion"

    "ten hundred myriad tryllion quintyllion sextyllion septyllion octyllion"

    Returns: "one myriad myllion septyllion nonyllion"

  35. "ten hundred myriad myllion byllion tryllion sextyllion octyllion nonyllion"

    "ten hundred myllion byllion tryllion quadryllion quintyllion sextyllion"

    Returns: "one hundred myllion byllion tryllion sextyllion septyllion octyllion nonyllion"

  36. "ten myllion byllion"

    "one"

    Returns: "ten myllion byllion"

  37. "ten hundred quadryllion quintyllion sextyllion septyllion octyllion"

    "one octyllion"

    Returns: "ten hundred quadryllion quintyllion sextyllion septyllion nonyllion"

  38. "ten hundred byllion tryllion quadryllion quintyllion sextyllion octyllion"

    "ten myriad myllion tryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "one tryllion quintyllion sextyllion octyllion decyllion"

  39. "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion nonyllion"

    "ten myllion quadryllion sextyllion"

    Returns: "one myllion quadryllion sextyllion octyllion nonyllion"

  40. "one hundred myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "ten myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion decyllion"

  41. "one sextyllion nonyllion"

    "one"

    Returns: "one sextyllion nonyllion"

  42. "ten hundred myriad myllion tryllion quadryllion quintyllion octyllion nonyllion"

    "one myriad byllion quintyllion sextyllion septyllion octyllion"

    Returns: "ten hundred quintyllion octyllion decyllion"

  43. "one myllion byllion quadryllion quintyllion sextyllion octyllion nonyllion"

    "ten myllion byllion tryllion octyllion"

    Returns: "ten byllion septyllion decyllion"

  44. "one"

    "one myriad byllion tryllion octyllion nonyllion"

    Returns: "one myriad byllion tryllion octyllion nonyllion"

  45. "ten hundred myriad myllion byllion tryllion quadryllion sextyllion septyllion octyllion nonyllion"

    "ten myllion byllion tryllion septyllion nonyllion"

    Returns: "one myllion byllion tryllion quintyllion sextyllion nonyllion decyllion"

  46. "ten hundred myriad myllion byllion tryllion quintyllion sextyllion septyllion nonyllion"

    "ten hundred myllion tryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "one hundred myllion tryllion quadryllion sextyllion septyllion nonyllion decyllion"

  47. "one hundred myriad myllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    "ten hundred myriad myllion byllion quadryllion nonyllion"

    Returns: "ten myriad myllion quadryllion nonyllion decyllion"

  48. "one hundred myriad myllion byllion tryllion quintyllion sextyllion nonyllion"

    "ten myriad myllion byllion tryllion quadryllion quintyllion septyllion octyllion nonyllion"

    Returns: "ten hundred myllion byllion tryllion quintyllion nonyllion decyllion"

  49. "one tryllion septyllion octyllion"

    "one hundred myriad byllion septyllion octyllion nonyllion"

    Returns: "one hundred myriad byllion tryllion octyllion decyllion"

  50. "ten myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    "one myllion sextyllion octyllion"

    Returns: "ten myriad sextyllion octyllion decyllion"

  51. "ten tryllion sextyllion septyllion nonyllion"

    "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "one tryllion sextyllion septyllion nonyllion decyllion"

  52. "one"

    "one octyllion"

    Returns: "one octyllion"

  53. "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion"

    "one"

    Returns: "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion"

  54. "one myriad tryllion quintyllion"

    "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    Returns: "ten hundred tryllion quintyllion decyllion"

  55. "ten quintyllion septyllion octyllion"

    "ten myriad myllion quadryllion quintyllion sextyllion septyllion nonyllion"

    Returns: "one hundred myriad myllion quadryllion septyllion decyllion"

  56. "ten hundred byllion quadryllion quintyllion septyllion octyllion"

    "ten hundred myllion"

    Returns: "one hundred myriad myllion byllion quadryllion quintyllion septyllion octyllion"

  57. "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    "ten hundred myriad myllion quadryllion quintyllion sextyllion octyllion"

    Returns: "one hundred myriad myllion quadryllion quintyllion sextyllion octyllion decyllion"

  58. "ten hundred myriad myllion byllion tryllion quadryllion quintyllion sextyllion septyllion octyllion nonyllion"

    "one hundred"

    Returns: "ten decyllion"

  59. "one"

    "one hundred"

    Returns: "one hundred"

  60. "one myriad"

    "one myllion"

    Returns: "one myriad myllion"

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