Statistics

Problem Statement for "TheNumberGame"

Problem Statement

Manao has recently invented a brand new game called The Number Game. He usually plays this game against his friend.

Initially, Manao has an integer A and his friend has an integer B. Note that neither A nor B contain a zero digit in their base 10 representation. The players make moves alternatively with Manao starting first. In each move, the player can either reverse his current number, or he can divide it by 10 (using integer division). For example, if the current number is 12849, the player can either reverse it to obtain 94821, or he can divide it by 10 to obtain 1284. Note that we always round down when using integer division. Also note that each player is only allowed to change his own number, and not the number of the other player.

If after some move the players' numbers become equal, Manao is declared the winner. If after 1000 moves (that is, 500 moves by Manao and 500 by his friend) Manao has not won, he loses. Given A and B, determine whether Manao would win if both players play optimally. Return "Manao wins" or "Manao loses" accordingly.

Definition

Class:
TheNumberGame
Method:
determineOutcome
Parameters:
int, int
Returns:
String
Method signature:
String determineOutcome(int A, int B)
(be sure your method is public)

Constraints

  • A will be between 1 and 999,999,999, inclusive.
  • B will be between 1 and 999,999,999, inclusive.
  • A and B will not contain a zero digit in base 10 representation.
  • A and B will be distinct.

Examples

  1. 45

    4

    Returns: "Manao wins"

    Manao can win in one move by dividing his number by 10.

  2. 45

    5

    Returns: "Manao wins"

    There are several possible scenarios this game can follow: Manao divides by 10 and obtains 4. Now his opponent can reverse his number and obtain 5 again. Obviously, no matter what Manao does in his next 499 moves, his opponent can evade him. Manao reverses his number and obtains 54. His opponent reverses his 5. Manao divides 54 by 10 and obtains 5, thus making the numbers equal Manao reverses his number and obtains 54. His opponent divides by 10 and obtains zero. Manao will win in three moves, dividing his number by 10 twice. Obviously, Manao will not choose to divide by 10 in his first move and will win.

  3. 99

    123

    Returns: "Manao loses"

    No matter how Manao plays, the opponent can perform reverse moves until the end of the game.

  4. 2356236

    5666

    Returns: "Manao loses"

  5. 11

    1

    Returns: "Manao wins"

  6. 12

    21

    Returns: "Manao wins"

  7. 123

    231

    Returns: "Manao loses"

  8. 123456789

    987654321

    Returns: "Manao wins"

  9. 123456789

    512346789

    Returns: "Manao loses"

  10. 446

    646

    Returns: "Manao loses"

  11. 446

    464

    Returns: "Manao loses"

  12. 446

    644

    Returns: "Manao wins"

  13. 7347837

    325

    Returns: "Manao loses"

  14. 7347837

    837

    Returns: "Manao wins"

  15. 611

    61

    Returns: "Manao wins"

  16. 123536363

    363

    Returns: "Manao wins"

  17. 995432553

    543

    Returns: "Manao wins"

  18. 995432553

    234

    Returns: "Manao wins"

  19. 987987789

    987

    Returns: "Manao wins"

  20. 978978789

    879

    Returns: "Manao wins"

  21. 314159265

    415

    Returns: "Manao wins"

  22. 314159265

    295

    Returns: "Manao wins"

  23. 8442

    4221

    Returns: "Manao loses"

  24. 8442

    42

    Returns: "Manao wins"

  25. 866395753

    6639575

    Returns: "Manao wins"

  26. 572681512

    26

    Returns: "Manao wins"

  27. 212321312

    33221

    Returns: "Manao loses"

  28. 212321312

    2212

    Returns: "Manao loses"

  29. 212321312

    213

    Returns: "Manao wins"

  30. 212321312

    21312

    Returns: "Manao wins"

  31. 212321312

    32131

    Returns: "Manao wins"

  32. 919244822

    44291

    Returns: "Manao wins"

  33. 824216852

    258612428

    Returns: "Manao wins"

  34. 258612428

    824216852

    Returns: "Manao wins"

  35. 126

    62

    Returns: "Manao wins"

  36. 76532791

    52369717

    Returns: "Manao loses"

  37. 811934182

    934818211

    Returns: "Manao loses"

  38. 8512658

    3752381

    Returns: "Manao loses"

  39. 2179425

    43785444

    Returns: "Manao loses"

  40. 1

    2

    Returns: "Manao loses"

  41. 111

    1

    Returns: "Manao wins"

  42. 44784278

    5129525

    Returns: "Manao loses"

  43. 64844626

    4462

    Returns: "Manao wins"

  44. 724582652

    245826

    Returns: "Manao wins"

  45. 276464629

    646

    Returns: "Manao wins"

  46. 276464629

    646467

    Returns: "Manao wins"

  47. 472246289

    64

    Returns: "Manao wins"

  48. 999999999

    92

    Returns: "Manao loses"

  49. 999999999

    9999

    Returns: "Manao wins"

  50. 999999999

    99999999

    Returns: "Manao wins"

  51. 123456789

    87654321

    Returns: "Manao wins"

  52. 12345678

    2345678

    Returns: "Manao wins"

  53. 123456789

    765

    Returns: "Manao wins"

  54. 12121

    212

    Returns: "Manao wins"

  55. 12345

    32

    Returns: "Manao wins"

  56. 1234

    24

    Returns: "Manao loses"

  57. 123

    321

    Returns: "Manao wins"

  58. 123

    32

    Returns: "Manao wins"

  59. 544

    45

    Returns: "Manao wins"

  60. 123

    21

    Returns: "Manao wins"

  61. 123456789

    8765

    Returns: "Manao wins"

  62. 1222

    221

    Returns: "Manao wins"

  63. 1234

    4321

    Returns: "Manao wins"

  64. 4321

    1234

    Returns: "Manao wins"

  65. 321

    123

    Returns: "Manao wins"

  66. 123

    69

    Returns: "Manao loses"

  67. 444

    4

    Returns: "Manao wins"

  68. 1234

    34

    Returns: "Manao wins"

  69. 1111

    11

    Returns: "Manao wins"

  70. 19

    91

    Returns: "Manao wins"

  71. 41679

    976

    Returns: "Manao wins"

  72. 12345

    23

    Returns: "Manao wins"

  73. 11

    111

    Returns: "Manao loses"

  74. 983625176

    15263

    Returns: "Manao wins"

  75. 1234567

    543

    Returns: "Manao wins"

  76. 545

    455

    Returns: "Manao loses"

  77. 14321

    1234

    Returns: "Manao wins"

  78. 11111122

    21

    Returns: "Manao wins"

  79. 12345

    54321

    Returns: "Manao wins"

  80. 1

    11

    Returns: "Manao loses"

  81. 1221

    2112

    Returns: "Manao loses"

  82. 234

    432

    Returns: "Manao wins"

  83. 123445

    344

    Returns: "Manao wins"

  84. 2345

    43

    Returns: "Manao wins"

  85. 132

    12

    Returns: "Manao loses"

  86. 12345

    432

    Returns: "Manao wins"

  87. 34

    43

    Returns: "Manao wins"

  88. 13161

    613

    Returns: "Manao wins"

  89. 26

    62

    Returns: "Manao wins"

  90. 31113

    111

    Returns: "Manao wins"

  91. 1234

    43

    Returns: "Manao wins"

  92. 4567

    54

    Returns: "Manao wins"

  93. 325134

    33254

    Returns: "Manao loses"

  94. 1

    111111

    Returns: "Manao loses"

  95. 2122334

    22233

    Returns: "Manao loses"

  96. 455

    5

    Returns: "Manao wins"

  97. 123

    12

    Returns: "Manao wins"

  98. 1234

    32

    Returns: "Manao wins"

  99. 45

    54

    Returns: "Manao wins"

  100. 1

    99

    Returns: "Manao loses"

  101. 54321

    12345

    Returns: "Manao wins"

  102. 1234

    123

    Returns: "Manao wins"

  103. 245

    45

    Returns: "Manao wins"

  104. 121213

    1213

    Returns: "Manao wins"

  105. 1234

    21

    Returns: "Manao wins"

  106. 3112

    21

    Returns: "Manao wins"

  107. 12345666

    456

    Returns: "Manao wins"

  108. 154

    45

    Returns: "Manao wins"

  109. 32

    23

    Returns: "Manao wins"

  110. 2

    1

    Returns: "Manao loses"

  111. 2325

    35

    Returns: "Manao loses"

  112. 1234

    321

    Returns: "Manao wins"

  113. 432

    43

    Returns: "Manao wins"

  114. 75157

    515

    Returns: "Manao wins"

  115. 451

    54

    Returns: "Manao wins"

  116. 123456789

    567

    Returns: "Manao wins"

  117. 455

    45

    Returns: "Manao wins"

  118. 165

    65

    Returns: "Manao wins"

  119. 4588

    45

    Returns: "Manao wins"

  120. 3212

    123

    Returns: "Manao wins"

  121. 123

    23

    Returns: "Manao wins"

  122. 123456789

    23456789

    Returns: "Manao wins"

  123. 999999999

    9

    Returns: "Manao wins"

  124. 1112111

    11211

    Returns: "Manao wins"

  125. 123456789

    214365879

    Returns: "Manao loses"

  126. 999876999

    9876

    Returns: "Manao wins"

  127. 999998999

    9999899

    Returns: "Manao wins"

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: