Statistics

Problem Statement for "DivisiblePermutations"

Problem Statement

We define a permutation of an integer N as an integer that has the exact same digits as N, but possibly in a different order. Two permutations of N are considered different if the numbers they represent are not the same. For example, the set of all different permutations of the number N = 313 is {133, 313, 331}.

Given a String N and an int M, determine the number of different permutations of N that are divisible by M.

Definition

Class:
DivisiblePermutations
Method:
count
Parameters:
String, int
Returns:
long
Method signature:
long count(String N, int M)
(be sure your method is public)

Constraints

  • N will contain between 1 and 15 non-zero digits ('1'-'9'), inclusive.
  • M will be between 1 and 50, inclusive.

Examples

  1. "133"

    7

    Returns: 1

    There are three permutations of 133 (133, 313, 331), but only 133 is divisible by 7.

  2. "2753"

    5

    Returns: 6

    The permutations of 2753 that are divisible by 5 are 2375, 2735, 3275, 3725, 7235 and 7325.

  3. "1112225"

    5

    Returns: 20

  4. "123456789"

    17

    Returns: 21271

  5. "987654321999999"

    39

    Returns: 19960896

  6. "1"

    2

    Returns: 0

  7. "999999999999999"

    9

    Returns: 1

  8. "999999999999999"

    1

    Returns: 1

  9. "999999999999999"

    2

    Returns: 0

  10. "7"

    7

    Returns: 1

  11. "7"

    5

    Returns: 0

  12. "71"

    1

    Returns: 2

  13. "72"

    3

    Returns: 2

  14. "987654321987654"

    1

    Returns: 20432412000

  15. "987654321987654"

    2

    Returns: 9535125600

  16. "987654321987654"

    3

    Returns: 20432412000

  17. "987654321987654"

    9

    Returns: 0

  18. "987654321987654"

    11

    Returns: 1860667200

  19. "987654321987654"

    17

    Returns: 1201908570

  20. "987654321987654"

    50

    Returns: 0

  21. "987654321987654"

    49

    Returns: 416980651

  22. "987654321987654"

    47

    Returns: 434727697

  23. "57113725698779"

    11

    Returns: 42071400

  24. "321166"

    13

    Returns: 12

  25. "4"

    46

    Returns: 0

  26. "5163449686"

    32

    Returns: 11540

  27. "297386725276"

    48

    Returns: 0

  28. "17233"

    8

    Returns: 3

  29. "9"

    15

    Returns: 0

  30. "754446927783"

    42

    Returns: 950496

  31. "5"

    4

    Returns: 0

  32. "6"

    31

    Returns: 0

  33. "1789"

    50

    Returns: 0

  34. "3137714858"

    42

    Returns: 0

  35. "4443977371"

    17

    Returns: 2969

  36. "98162841628"

    5

    Returns: 0

  37. "5773414292"

    22

    Returns: 14400

  38. "113313143565853"

    30

    Returns: 0

  39. "9"

    41

    Returns: 0

  40. "113529317896"

    9

    Returns: 0

  41. "989957223297229"

    20

    Returns: 0

  42. "14321647835149"

    33

    Returns: 0

  43. "8712829"

    6

    Returns: 0

  44. "623659"

    40

    Returns: 0

  45. "662883374628947"

    24

    Returns: 0

  46. "9118463136675"

    16

    Returns: 4425120

  47. "6595625"

    46

    Returns: 6

  48. "767993273"

    13

    Returns: 1156

  49. "295691123255225"

    34

    Returns: 2670654

  50. "498241"

    32

    Returns: 21

  51. "3995977"

    31

    Returns: 13

  52. "63"

    7

    Returns: 1

  53. "793579949546585"

    28

    Returns: 7720244

  54. "612677154322929"

    45

    Returns: 0

  55. "974775963484298"

    40

    Returns: 0

  56. "823689438517296"

    44

    Returns: 332224200

  57. "593122955657244"

    1

    Returns: 2270268000

  58. "326881255488785"

    42

    Returns: 0

  59. "462627765381156"

    29

    Returns: 117426948

  60. "755418619235526"

    38

    Returns: 143384907

  61. "927437473988247"

    46

    Returns: 11515579

  62. "994938585878792"

    16

    Returns: 22245300

  63. "649369117645183"

    30

    Returns: 0

  64. "722598674738743"

    13

    Returns: 261918765

  65. "392546449958534"

    19

    Returns: 39828401

  66. "542883921525521"

    26

    Returns: 20377814

  67. "292154732769956"

    14

    Returns: 259484120

  68. "997661224423129"

    17

    Returns: 66773001

  69. "493216396584441"

    49

    Returns: 69504155

  70. "845883316624743"

    22

    Returns: 162640800

  71. "692737935531985"

    29

    Returns: 104375029

  72. "725773548515399"

    13

    Returns: 174674382

  73. "868482581124251"

    46

    Returns: 10968374

  74. "834937776637446"

    31

    Returns: 8136015

  75. "799217226723546"

    40

    Returns: 0

  76. "853751555994681"

    26

    Returns: 27939234

  77. "352668338218384"

    46

    Returns: 14805100

  78. "174258988287556"

    41

    Returns: 55307610

  79. "348865746965852"

    36

    Returns: 0

  80. "648712948548431"

    8

    Returns: 731808000

  81. "798994279857884"

    39

    Returns: 0

  82. "454573349997578"

    2

    Returns: 134534400

  83. "111112222233333"

    49

    Returns: 15443

  84. "111111123333333"

    49

    Returns: 1056

  85. "111111113333333"

    49

    Returns: 133

  86. "123456789123456"

    49

    Returns: 416987439

  87. "123456789127456"

    49

    Returns: 416988138

  88. "888888888888888"

    2

    Returns: 1

  89. "888888888888887"

    2

    Returns: 14

  90. "988888888888888"

    2

    Returns: 14

  91. "999999999999999"

    9

    Returns: 1

  92. "999999999999999"

    3

    Returns: 1

  93. "199999999999999"

    9

    Returns: 0

  94. "123456789878765"

    3

    Returns: 0

  95. "342239829657425"

    47

    Returns: 72453064

  96. "998877665544321"

    11

    Returns: 1860667200

  97. "123456789123456"

    1

    Returns: 20432412000

  98. "123456789123456"

    49

    Returns: 416987439

  99. "123456789123456"

    2

    Returns: 9535125600

  100. "123456781234569"

    1

    Returns: 20432412000

  101. "123456789912345"

    49

    Returns: 416973824

  102. "123456789876543"

    17

    Returns: 1201902822

  103. "123456789123456"

    5

    Returns: 2724321600

  104. "123456789123456"

    3

    Returns: 20432412000

  105. "123456789123456"

    41

    Returns: 498015135

  106. "778223491265334"

    29

    Returns: 313149050

  107. "987654321234567"

    49

    Returns: 416986862

  108. "112233445566789"

    39

    Returns: 1571586219

  109. "123456789123456"

    15

    Returns: 2724321600

  110. "123456789123477"

    47

    Returns: 289811662

  111. "987654321999999"

    39

    Returns: 19960896

  112. "987654321987654"

    47

    Returns: 434727697

  113. "123456789123456"

    48

    Returns: 1212472800

  114. "123456789243876"

    49

    Returns: 416973395

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