Statistics

Problem Statement for "SimpleGuess"

Problem Statement

A cat and a rabbit are playing a simple number guessing game. The cat chose two different positive integers X and Y. He then told the rabbit several numbers. One of those numbers was X + Y and another was X - Y. The others were simply made up.

The rabbit thinks the cat prefers large numbers. Given a int[] hints containing the numbers the cat told the rabbit, return the largest possible value of X * Y.

Definition

Class:
SimpleGuess
Method:
getMaximum
Parameters:
int[]
Returns:
int
Method signature:
int getMaximum(int[] hints)
(be sure your method is public)

Constraints

  • hints will contain between 2 and 50 elements, inclusive.
  • Each element of hints will be between 1 and 100, inclusive.
  • All elements of hints will be distinct.
  • There will exist at least one pair of positive integers (X, Y) such that both X + Y and X - Y are elements of hints.

Examples

  1. { 1, 4, 5 }

    Returns: 6

    The rabbit can determine that (X, Y) = (3, 2).

  2. { 1, 4, 5, 8 }

    Returns: 12

    Possible pairs (X, Y) are (3, 2) and (6, 2). The values of X * Y are 6 and 12, respectively, and the largest is 12.

  3. { 9, 8, 7, 6, 5, 4, 3, 2, 1 }

    Returns: 20

  4. { 2, 100 }

    Returns: 2499

  5. { 50, 58, 47, 57, 40 }

    Returns: 441

  6. { 1, 3 }

    Returns: 2

  7. { 3, 1 }

    Returns: 2

  8. { 1, 99 }

    Returns: 2450

  9. { 99, 1 }

    Returns: 2450

  10. { 97, 99 }

    Returns: 98

  11. { 99, 97 }

    Returns: 98

  12. { 2, 4 }

    Returns: 3

  13. { 4, 2 }

    Returns: 3

  14. { 100, 2 }

    Returns: 2499

  15. { 98, 100 }

    Returns: 99

  16. { 100, 98 }

    Returns: 99

  17. { 4, 89, 12, 76, 91, 80 }

    Returns: 1596

  18. { 2, 6, 5, 11, 9, 10, 4, 7 }

    Returns: 24

  19. { 48, 12, 30, 39, 6, 14, 11, 50, 16, 20, 49, 24, 22, 8, 7, 36, 9, 15, 46, 4, 42, 28, 5, 17, 29, 27, 26, 45, 34, 21, 33, 18, 2, 25, 41, 10, 35, 13, 3, 43, 40, 44, 32, 1, 19, 37, 47, 38, 31, 23 }

    Returns: 624

  20. { 100, 56, 59, 91, 60, 99, 67, 71, 95, 64, 90, 58, 52, 65, 69, 85, 94, 80, 92, 81, 79, 63, 89, 76, 77, 98, 62, 87, 73, 86, 82, 88, 83, 75, 61, 66, 57, 53, 84, 74, 93, 51, 78, 72, 97, 55, 70, 68, 96, 54 }

    Returns: 1824

  21. { 77, 61, 21, 13, 81, 69, 17, 95, 83, 39, 3, 75, 91, 99, 57, 25, 49, 97, 19, 33, 11, 37, 51, 89, 41, 85, 65, 45, 71, 59, 1, 43, 15, 67, 35, 5, 79, 93, 87, 7, 47, 73, 23, 53, 55, 29, 27, 63, 31, 9 }

    Returns: 2450

  22. { 82, 88, 38, 16, 54, 6, 2, 94, 84, 56, 34, 72, 92, 4, 66, 76, 100, 14, 60, 48, 90, 50, 74, 70, 18, 44, 24, 46, 68, 8, 40, 26, 32, 10, 42, 96, 12, 62, 22, 80, 78, 30, 86, 58, 52, 36, 20, 98, 28, 64 }

    Returns: 2499

  23. { 1, 3 }

    Returns: 2

  24. { 1, 2, 3 }

    Returns: 2

  25. { 2, 4 }

    Returns: 3

  26. { 1, 2, 4 }

    Returns: 3

  27. { 1, 3, 4 }

    Returns: 2

  28. { 2, 3, 4 }

    Returns: 3

  29. { 1, 2, 3, 4 }

    Returns: 3

  30. { 1, 5 }

    Returns: 6

  31. { 1, 2, 5 }

    Returns: 6

  32. { 3, 5 }

    Returns: 4

  33. { 1, 3, 5 }

    Returns: 6

  34. { 2, 3, 5 }

    Returns: 4

  35. { 1, 2, 3, 5 }

    Returns: 6

  36. { 1, 4, 5 }

    Returns: 6

  37. { 2, 4, 5 }

    Returns: 3

  38. { 1, 2, 4, 5 }

    Returns: 6

  39. { 3, 4, 5 }

    Returns: 4

  40. { 1, 3, 4, 5 }

    Returns: 6

  41. { 2, 3, 4, 5 }

    Returns: 4

  42. { 1, 2, 3, 4, 5 }

    Returns: 6

  43. { 2, 6 }

    Returns: 8

  44. { 1, 2, 6 }

    Returns: 8

  45. { 1, 3, 6 }

    Returns: 2

  46. { 2, 3, 6 }

    Returns: 8

  47. { 1, 2, 3, 6 }

    Returns: 8

  48. { 4, 6 }

    Returns: 5

  49. { 1, 4, 6 }

    Returns: 5

  50. { 2, 4, 6 }

    Returns: 8

  51. { 1, 2, 4, 6 }

    Returns: 8

  52. { 3, 4, 6 }

    Returns: 5

  53. { 1, 3, 4, 6 }

    Returns: 5

  54. { 2, 3, 4, 6 }

    Returns: 8

  55. { 1, 2, 3, 4, 6 }

    Returns: 8

  56. { 1, 5, 6 }

    Returns: 6

  57. { 2, 5, 6 }

    Returns: 8

  58. { 1, 2, 5, 6 }

    Returns: 8

  59. { 3, 5, 6 }

    Returns: 4

  60. { 1, 3, 5, 6 }

    Returns: 6

  61. { 2, 3, 5, 6 }

    Returns: 8

  62. { 1, 2, 3, 5, 6 }

    Returns: 8

  63. { 4, 5, 6 }

    Returns: 5

  64. { 1, 4, 5, 6 }

    Returns: 6

  65. { 2, 4, 5, 6 }

    Returns: 8

  66. { 1, 2, 4, 5, 6 }

    Returns: 8

  67. { 3, 4, 5, 6 }

    Returns: 5

  68. { 1, 3, 4, 5, 6 }

    Returns: 6

  69. { 2, 3, 4, 5, 6 }

    Returns: 8

  70. { 1, 2, 3, 4, 5, 6 }

    Returns: 8

  71. { 14, 92, 85, 58, 65, 69, 73, 47, 76, 83, 61, 49, 64, 55, 43, 93, 59, 86, 32, 68, 77, 75, 95, 50, 72, 97, 30, 71, 67, 89, 41 }

    Returns: 2067

  72. { 51, 10, 35, 47, 43, 63, 14, 59, 57, 77, 12, 81, 8, 67, 37, 33, 69, 31, 91 }

    Returns: 1830

  73. { 68, 33, 60, 25, 11, 62, 46, 21, 41, 32, 37, 70, 42, 36, 45, 51, 50, 23, 30, 19, 38, 74, 56, 40, 66, 44, 72, 64, 48, 52, 58, 27, 54, 7, 34, 28, 76 }

    Returns: 1248

  74. { 30, 92, 80, 36, 44, 7, 46, 88, 32, 5, 86, 82, 54, 56, 76, 78, 15, 3, 60, 9, 90, 13, 38, 68, 72, 34, 58, 48 }

    Returns: 1891

  75. { 15, 83, 28, 19, 49, 77, 33, 65, 17, 71, 35, 45, 37, 67, 23, 56, 81, 75, 51, 43, 73, 41, 31, 79, 53, 63, 57, 47, 69, 39, 21, 54, 27, 61 }

    Returns: 1666

  76. { 41, 62, 45, 56, 58, 60, 39, 52, 64 }

    Returns: 348

  77. { 68, 66, 60, 58, 42, 40, 34, 32, 28, 24, 13, 11, 7, 5 }

    Returns: 1012

  78. { 9, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 34, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82 }

    Returns: 1617

  79. { 15, 17, 19, 21, 23, 29, 31, 33, 37, 39, 43, 47, 48, 49, 50, 52, 54, 55, 56, 57, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 77, 81, 83, 85, 87, 89, 93, 95, 97 }

    Returns: 2296

  80. { 7, 26, 82, 70, 76, 92, 4, 98, 18, 84, 40, 30, 80, 52, 66, 42, 5, 62, 46, 10, 86, 72, 68, 28, 48, 60, 44, 54, 74, 12, 20, 16 }

    Returns: 2397

  81. { 1, 5, 27, 52, 53, 54, 56, 64, 68, 70, 72, 76, 78, 80, 81, 82, 86, 88, 94, 96, 98 }

    Returns: 1725

  82. { 9, 28, 22, 16, 50, 11, 30, 5, 20, 3, 32, 15, 8, 54 }

    Returns: 713

  83. { 77, 85, 87, 79, 75, 36, 91, 83, 89, 93, 95, 81, 73, 97 }

    Returns: 1020

  84. { 60, 68, 65, 80, 84, 78, 31, 58, 96, 51, 47, 56, 88, 11, 61, 86, 70, 25, 13, 35, 82, 50, 98 }

    Returns: 1776

  85. { 7, 39, 15, 9, 35, 29, 21, 13, 19, 31, 82, 27, 25, 37, 33, 11 }

    Returns: 368

  86. { 18, 68, 62, 46, 60, 42, 48, 44, 36, 24, 30, 28, 32, 56, 40, 64, 20, 58, 34, 22, 66, 26, 52, 54, 38, 50 }

    Returns: 1075

  87. { 9, 5, 18, 7, 10, 16 }

    Returns: 56

  88. { 15, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 35, 36, 41, 42, 43, 45, 49, 51, 55, 57, 59, 61, 63, 65, 67, 71, 73, 77, 79, 81, 83, 85, 87, 89 }

    Returns: 1924

  89. {2, 6, 11 }

    Returns: 8

  90. {1, 3, 14 }

    Returns: 2

  91. {4, 2, 9 }

    Returns: 3

  92. {1, 3, 20 }

    Returns: 2

  93. {1, 100, 5 }

    Returns: 6

  94. {1, 4, 5 }

    Returns: 6

  95. {100, 80, 3 }

    Returns: 900

  96. {1, 3, 4 }

    Returns: 2

  97. {2, 98, 99 }

    Returns: 2400

  98. {98, 51, 3, 1 }

    Returns: 650

  99. {5, 1 }

    Returns: 6

  100. {45, 8, 43 }

    Returns: 44

  101. {11, 8, 2 }

    Returns: 15

  102. {1, 6, 100 }

    Returns: 2491

  103. {12, 7, 10, 1 }

    Returns: 12

  104. {100, 1, 3 }

    Returns: 2

  105. {1, 2, 14 }

    Returns: 48

  106. {2, 4, 7 }

    Returns: 3

  107. {1, 5, 8 }

    Returns: 6

  108. {50, 58, 47, 57, 40 }

    Returns: 441

  109. {10, 2, 1 }

    Returns: 24

  110. {1, 4, 5, 8 }

    Returns: 12

  111. {1, 4, 5, 66 }

    Returns: 1085

  112. {1, 3, 8 }

    Returns: 2

  113. {100, 3, 1 }

    Returns: 2

  114. {1, 2, 3, 4, 5, 6, 10, 50 }

    Returns: 624

  115. {2, 4, 9 }

    Returns: 3

  116. {1, 5, 10 }

    Returns: 6

  117. {100, 99, 1 }

    Returns: 2450

  118. {1, 5, 100 }

    Returns: 6

  119. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50 }

    Returns: 624

  120. {1, 3, 100 }

    Returns: 2

  121. {1, 4, 6 }

    Returns: 5

  122. {1, 6, 8 }

    Returns: 7

  123. {3, 7, 10 }

    Returns: 10

  124. {2, 15, 52, 53 }

    Returns: 675

  125. {4, 7, 13 }

    Returns: 30

  126. {2, 7, 4 }

    Returns: 3

  127. {2, 100 }

    Returns: 2499

  128. {9, 8, 2 }

    Returns: 15

  129. {41, 8, 2 }

    Returns: 15

  130. {3, 16, 5 }

    Returns: 4

  131. {1, 3, 6 }

    Returns: 2

  132. {2, 3, 8, 99 }

    Returns: 2448

  133. {8, 100, 2, 1 }

    Returns: 2499

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