Statistics

Problem Statement for "ChildlessNumbers"

Problem Statement

Let D(X) denote the sum of digits of the positive integer X. For example, D(4007) = 4 + 0 + 0 + 7 = 11.

Take any positive integer X, and let Y = X / D(X). If Y is an integer, we say that Y is the parent of X (and that X is a child of Y). For example, if X=12 then X / D(X) = 12 / (1+2) = 4, hence 4 is the parent of 12.

Note that multiple numbers can have the same parent. For example, 4 is also the parent of 36, as 36/(3+6) = 36/9 = 4.

We say that a number Y is childless if there is no positive integer X such that Y is the parent of X.

You are given two ints A and B. Find and return the count of all childless numbers that lie between A and B, inclusive.

Definition

Class:
ChildlessNumbers
Method:
howMany
Parameters:
int, int
Returns:
int
Method signature:
int howMany(int A, int B)
(be sure your method is public)

Constraints

  • A will be between 1 and 1,000,000,000, inclusive.
  • B will be between A and 1,000,000,000, inclusive.
  • B-A will be between 0 and 10,000, inclusive.

Examples

  1. 4

    7

    Returns: 0

    Each of the numbers {4,5,6,7} has at least one child. For example, 54 / (5+4) = 6, hence 6 is not childless.

  2. 37

    37

    Returns: 0

    E.g., 333 / (3+3+3) = 37.

  3. 61

    65

    Returns: 3

    In this range there are three childless numbers: 62, 63, and 65. For the other two we have 732 / (7+3+2) = 732/12 = 61 and 320 / (3+2+0) = 320/5 = 64.

  4. 275

    300

    Returns: 1

    The only childless number in this range is 276.

  5. 999990000

    1000000000

    Returns: 1950

  6. 24684440

    24694440

    Returns: 6504

  7. 796878566

    796888566

    Returns: 5990

  8. 246889265

    246899265

    Returns: 6714

    Largest possible output.

  9. 600240035

    600250035

    Returns: 4015

  10. 1

    61

    Returns: 0

  11. 123

    1234

    Returns: 123

  12. 351335515

    351344526

    Returns: 1405

  13. 528977286

    528987005

    Returns: 1295

  14. 528960940

    528970618

    Returns: 1371

  15. 565076706

    565085728

    Returns: 1417

  16. 442067845

    442076950

    Returns: 2251

  17. 961895748

    961904910

    Returns: 906

  18. 775735046

    775744477

    Returns: 1284

  19. 278346336

    278355401

    Returns: 1305

  20. 257178195

    257188149

    Returns: 2043

  21. 902190830

    902200076

    Returns: 1556

  22. 725290028

    725299440

    Returns: 525

  23. 406229757

    406239020

    Returns: 889

  24. 467189414

    467199296

    Returns: 3084

  25. 63910586

    63919677

    Returns: 1442

  26. 85332141

    85341410

    Returns: 1097

  27. 492764954

    492774046

    Returns: 1438

  28. 464746988

    464756249

    Returns: 811

  29. 603290547

    603300358

    Returns: 1256

  30. 296892983

    296902676

    Returns: 3901

  31. 803175278

    803184488

    Returns: 2353

  32. 214912744

    214922399

    Returns: 2352

  33. 340977766

    340987588

    Returns: 2112

  34. 414128404

    414137473

    Returns: 3018

  35. 761144736

    761154271

    Returns: 1088

  36. 451108100

    451117100

    Returns: 1650

  37. 997454526

    997464025

    Returns: 2027

  38. 407297265

    407306442

    Returns: 1151

  39. 770251789

    770261612

    Returns: 1366

  40. 527905756

    527914777

    Returns: 1622

  41. 202945158

    202954504

    Returns: 768

  42. 414612527

    414622395

    Returns: 2491

  43. 77452467

    77461924

    Returns: 1282

  44. 131739827

    131748843

    Returns: 1938

  45. 707390900

    707400065

    Returns: 856

  46. 335226580

    335235887

    Returns: 1654

  47. 800534669

    800544111

    Returns: 2990

  48. 45837515

    45846949

    Returns: 1394

  49. 927960385

    927969700

    Returns: 1889

  50. 249227989

    249237894

    Returns: 3478

  51. 885857927

    885867183

    Returns: 1770

  52. 207764884

    207774832

    Returns: 3763

  53. 211551607

    211561224

    Returns: 3312

  54. 436228931

    436238581

    Returns: 936

  55. 22690928

    22700715

    Returns: 3556

  56. 217067930

    217077313

    Returns: 3535

  57. 895261871

    895271781

    Returns: 1362

  58. 687568321

    687577878

    Returns: 1558

  59. 335719561

    335728799

    Returns: 1395

  60. 920197459

    920207276

    Returns: 664

  61. 887825232

    887834270

    Returns: 1561

  62. 808568719

    808578169

    Returns: 2359

  63. 971902894

    971912231

    Returns: 1739

  64. 139388593

    139397863

    Returns: 925

  65. 29377021

    29386652

    Returns: 2309

  66. 285595860

    285604998

    Returns: 951

  67. 80470052

    80479564

    Returns: 3467

  68. 426363320

    426372571

    Returns: 2383

  69. 458686126

    458696071

    Returns: 825

  70. 839114445

    839123981

    Returns: 960

  71. 22729068

    22739067

    Returns: 3793

  72. 90976355

    90985904

    Returns: 1971

  73. 594207268

    594216282

    Returns: 2173

  74. 452450289

    452459927

    Returns: 3360

  75. 926013635

    926022710

    Returns: 1406

  76. 460148421

    460158182

    Returns: 545

  77. 510547903

    510557870

    Returns: 2280

  78. 941340139

    941349233

    Returns: 2093

  79. 111473196

    111482265

    Returns: 1925

  80. 667187816

    667197285

    Returns: 2489

  81. 389177008

    389186264

    Returns: 1922

  82. 64545658

    64554884

    Returns: 841

  83. 799481524

    799490766

    Returns: 4546

  84. 731982026

    731991140

    Returns: 1346

  85. 620241859

    620251622

    Returns: 1665

  86. 258688078

    258697252

    Returns: 1419

  87. 680666105

    680675973

    Returns: 1322

  88. 223440998

    223450193

    Returns: 1881

  89. 321940804

    321950658

    Returns: 1451

  90. 386920061

    386929443

    Returns: 1515

  91. 881775038

    881784297

    Returns: 1428

  92. 850152307

    850162266

    Returns: 862

  93. 600967234

    600976804

    Returns: 1538

  94. 206877322

    206887276

    Returns: 3209

  95. 813560941

    813570525

    Returns: 2158

  96. 565266145

    565275513

    Returns: 2238

  97. 846678419

    846688125

    Returns: 1748

  98. 74143003

    74152705

    Returns: 1750

  99. 858352832

    858362107

    Returns: 1697

  100. 950610321

    950619370

    Returns: 1056

  101. 435269929

    435279120

    Returns: 3562

  102. 96815209

    96824357

    Returns: 1466

  103. 337495332

    337504692

    Returns: 1436

  104. 613762382

    613771764

    Returns: 1986

  105. 760418416

    760427846

    Returns: 1692

  106. 362224294

    362233495

    Returns: 2314

  107. 737726465

    737736172

    Returns: 1340

  108. 136520361

    136529929

    Returns: 2399

  109. 282195070

    282204289

    Returns: 819

  110. 902563388

    902573199

    Returns: 998

  111. 785765956

    785775447

    Returns: 3577

  112. 1

    10000

    Returns: 1437

  113. 966660000

    966670000

    Returns: 971

    Requires checking sum of at least 93

  114. 900000000

    900010000

    Returns: 1429

  115. 999990000

    999999999

    Returns: 1950

  116. 100000000

    100010000

    Returns: 1794

  117. 90000000

    90010000

    Returns: 1429

  118. 999999000

    1000000000

    Returns: 192

  119. 912335671

    912345671

    Returns: 814

  120. 999989876

    999999875

    Returns: 1953

  121. 790829357

    790839357

    Returns: 2351

  122. 63

    63

    Returns: 1

  123. 999999990

    1000000000

    Returns: 1

  124. 999999990

    999999999

    Returns: 1

  125. 10

    10000

    Returns: 1437

  126. 999989999

    999999999

    Returns: 1950

  127. 981230000

    981232981

    Returns: 222

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