Statistics

Problem Statement for "PotatoGame"

Problem Statement

Taro and Hanako like potatoes very much. Today they decided to play Potato Game.

Initially there is a box containing n potatoes. Taro and Hanako alternate turns, and Taro goes first. In each turn, the player must eat some potatoes from the box. The number of eaten potatoes must be a power of four, i.e., 1, 4, 16, 64 and so on. The first player who cannot eat a valid number of potatoes loses. Return the name of the winner assuming that they both play optimally.

Definition

Class:
PotatoGame
Method:
theWinner
Parameters:
int
Returns:
String
Method signature:
String theWinner(int n)
(be sure your method is public)

Constraints

  • n will be between 1 and 1,000,000,000 (10^9), inclusive.

Examples

  1. 1

    Returns: "Taro"

    Taro will win if he eats 1 potato in the first turn.

  2. 2

    Returns: "Hanako"

    Taro must eat exactly 1 potato in the first turn. In the second turn, Hanako will eat 1 potato and she will win.

  3. 3

    Returns: "Taro"

  4. 4

    Returns: "Taro"

  5. 5

    Returns: "Hanako"

  6. 6

    Returns: "Taro"

  7. 7

    Returns: "Hanako"

  8. 8

    Returns: "Taro"

  9. 9

    Returns: "Taro"

  10. 1000000000

    Returns: "Hanako"

  11. 999999999

    Returns: "Taro"

  12. 999999998

    Returns: "Taro"

  13. 999999997

    Returns: "Hanako"

  14. 999999996

    Returns: "Taro"

  15. 999999995

    Returns: "Hanako"

  16. 999999994

    Returns: "Taro"

  17. 999999993

    Returns: "Taro"

  18. 999999992

    Returns: "Hanako"

  19. 536870909

    Returns: "Taro"

  20. 536870910

    Returns: "Hanako"

  21. 536870911

    Returns: "Taro"

  22. 536870912

    Returns: "Hanako"

  23. 536870913

    Returns: "Taro"

  24. 536870914

    Returns: "Taro"

  25. 536870915

    Returns: "Hanako"

  26. 73

    Returns: "Taro"

  27. 12

    Returns: "Hanako"

  28. 400

    Returns: "Hanako"

  29. 756

    Returns: "Taro"

  30. 9119

    Returns: "Taro"

  31. 6351

    Returns: "Taro"

  32. 52843

    Returns: "Taro"

  33. 18705

    Returns: "Hanako"

  34. 754108

    Returns: "Taro"

  35. 846393

    Returns: "Taro"

  36. 6118330

    Returns: "Hanako"

  37. 9932169

    Returns: "Taro"

  38. 83226917

    Returns: "Hanako"

  39. 95669847

    Returns: "Hanako"

  40. 877206980

    Returns: "Hanako"

  41. 501950427

    Returns: "Hanako"

  42. 9999998

    Returns: "Taro"

  43. 9999

    Returns: "Taro"

  44. 13

    Returns: "Taro"

  45. 22

    Returns: "Hanako"

  46. 102

    Returns: "Hanako"

  47. 19999999

    Returns: "Taro"

  48. 535432525

    Returns: "Hanako"

  49. 15

    Returns: "Hanako"

  50. 991829257

    Returns: "Hanako"

  51. 100000000

    Returns: "Hanako"

  52. 41432437

    Returns: "Hanako"

  53. 30

    Returns: "Hanako"

  54. 999966512

    Returns: "Hanako"

  55. 987345765

    Returns: "Hanako"

  56. 7605203

    Returns: "Taro"

  57. 444444444

    Returns: "Taro"

  58. 173

    Returns: "Taro"

  59. 10

    Returns: "Hanako"

  60. 987987987

    Returns: "Hanako"

  61. 974782859

    Returns: "Taro"

  62. 19

    Returns: "Taro"

  63. 998997992

    Returns: "Hanako"

  64. 67

    Returns: "Hanako"

  65. 34

    Returns: "Taro"

  66. 1324322

    Returns: "Hanako"

  67. 192

    Returns: "Hanako"

  68. 256

    Returns: "Taro"

  69. 500000000

    Returns: "Hanako"

  70. 7788

    Returns: "Taro"

  71. 1000

    Returns: "Hanako"

  72. 99988789

    Returns: "Taro"

  73. 388148910

    Returns: "Hanako"

  74. 200

    Returns: "Hanako"

  75. 35

    Returns: "Hanako"

  76. 17

    Returns: "Hanako"

  77. 10000009

    Returns: "Taro"

  78. 10000000

    Returns: "Hanako"

  79. 80

    Returns: "Hanako"

  80. 11478

    Returns: "Taro"

  81. 16

    Returns: "Taro"

  82. 13214

    Returns: "Taro"

  83. 334424233

    Returns: "Taro"

  84. 265353484

    Returns: "Taro"

  85. 100

    Returns: "Hanako"

  86. 999999

    Returns: "Taro"

  87. 14

    Returns: "Taro"

  88. 20

    Returns: "Hanako"

  89. 987998764

    Returns: "Taro"

  90. 25

    Returns: "Hanako"

  91. 998799634

    Returns: "Taro"

  92. 68

    Returns: "Taro"

  93. 18

    Returns: "Taro"

  94. 123456789

    Returns: "Taro"

  95. 334424238

    Returns: "Taro"

  96. 99

    Returns: "Taro"

  97. 987345998

    Returns: "Taro"

  98. 64

    Returns: "Taro"

  99. 174576865

    Returns: "Hanako"

  100. 354339

    Returns: "Taro"

  101. 949199136

    Returns: "Taro"

  102. 28

    Returns: "Taro"

  103. 32

    Returns: "Hanako"

  104. 18467

    Returns: "Hanako"

  105. 259

    Returns: "Taro"

  106. 131074

    Returns: "Taro"

  107. 989998898

    Returns: "Taro"

  108. 19169

    Returns: "Taro"

  109. 98742

    Returns: "Hanako"

  110. 999

    Returns: "Taro"

  111. 76

    Returns: "Taro"

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