Statistics

Problem Statement for "PackingBallsDiv2"

Problem Statement

We have R red, G green, and B blue balls. We want to divide them into as few packages as possible. Each package must contain 1, 2, or 3 balls. Additionally, each package must be either a "normal set" (all balls in the package have the same color), or a "variety set" (no two balls have the same color). Compute and return the smallest possible number of packages.

Definition

Class:
PackingBallsDiv2
Method:
minPacks
Parameters:
int, int, int
Returns:
int
Method signature:
int minPacks(int R, int G, int B)
(be sure your method is public)

Constraints

  • R, G, and B will each be between 1 and 100, inclusive.

Examples

  1. 4

    2

    4

    Returns: 4

    We have 4 red, 2 green, and 4 blue balls. Clearly, we need at least four packages to store 10 balls. One possibility of using exactly four packages looks as follows: RGB, RG, RR, BBB. (I.e., the first package has 1 ball of each color, the second package has a red and a green ball, and so on.)

  2. 1

    7

    1

    Returns: 3

    Here the only possible solution is to have one package with RGB and two packages with GGG each.

  3. 2

    3

    5

    Returns: 4

  4. 78

    53

    64

    Returns: 66

  5. 100

    100

    100

    Returns: 100

  6. 1

    1

    1

    Returns: 1

  7. 1

    1

    2

    Returns: 2

  8. 1

    1

    3

    Returns: 2

  9. 1

    1

    4

    Returns: 2

  10. 1

    1

    5

    Returns: 3

  11. 1

    2

    2

    Returns: 2

  12. 1

    2

    3

    Returns: 3

  13. 1

    2

    4

    Returns: 3

  14. 1

    2

    5

    Returns: 3

  15. 1

    3

    3

    Returns: 3

  16. 1

    3

    4

    Returns: 3

  17. 1

    3

    5

    Returns: 4

  18. 1

    4

    4

    Returns: 3

  19. 1

    4

    5

    Returns: 4

  20. 1

    5

    5

    Returns: 4

  21. 2

    2

    2

    Returns: 2

  22. 2

    2

    3

    Returns: 3

  23. 2

    2

    4

    Returns: 3

  24. 2

    2

    5

    Returns: 3

  25. 2

    3

    3

    Returns: 3

  26. 2

    3

    4

    Returns: 4

  27. 2

    4

    4

    Returns: 4

  28. 2

    4

    5

    Returns: 4

  29. 2

    5

    5

    Returns: 4

  30. 3

    3

    3

    Returns: 3

  31. 3

    3

    4

    Returns: 4

  32. 3

    3

    5

    Returns: 4

  33. 3

    4

    4

    Returns: 4

  34. 3

    4

    5

    Returns: 5

  35. 3

    5

    5

    Returns: 5

  36. 4

    4

    4

    Returns: 4

  37. 4

    4

    5

    Returns: 5

  38. 4

    5

    5

    Returns: 5

  39. 5

    5

    5

    Returns: 5

  40. 5

    8

    6

    Returns: 7

  41. 2

    1

    6

    Returns: 4

  42. 9

    10

    8

    Returns: 10

  43. 10

    7

    5

    Returns: 8

  44. 2

    5

    4

    Returns: 4

  45. 8

    1

    5

    Returns: 5

  46. 8

    2

    1

    Returns: 4

  47. 6

    3

    6

    Returns: 5

  48. 10

    3

    9

    Returns: 8

  49. 7

    7

    4

    Returns: 6

  50. 28

    88

    56

    Returns: 58

  51. 66

    17

    93

    Returns: 59

  52. 5

    4

    82

    Returns: 31

  53. 87

    69

    19

    Returns: 59

  54. 30

    91

    98

    Returns: 74

  55. 2

    57

    13

    Returns: 25

  56. 46

    30

    52

    Returns: 43

  57. 45

    11

    29

    Returns: 29

  58. 94

    43

    65

    Returns: 68

  59. 93

    90

    15

    Returns: 66

  60. 64

    70

    20

    Returns: 52

  61. 3

    53

    57

    Returns: 38

  62. 69

    95

    40

    Returns: 69

  63. 90

    99

    13

    Returns: 68

  64. 41

    42

    51

    Returns: 45

  65. 85

    58

    3

    Returns: 49

  66. 15

    41

    46

    Returns: 35

  67. 22

    34

    61

    Returns: 39

  68. 14

    93

    17

    Returns: 42

  69. 16

    71

    3

    Returns: 31

  70. 79

    72

    97

    Returns: 83

  71. 96

    71

    79

    Returns: 83

  72. 100

    76

    84

    Returns: 87

  73. 91

    96

    91

    Returns: 93

  74. 72

    99

    100

    Returns: 91

  75. 10

    10

    9

    Returns: 10

  76. 3

    3

    2

    Returns: 3

  77. 6

    6

    2

    Returns: 5

  78. 75

    50

    61

    Returns: 63

  79. 4

    3

    4

    Returns: 4

  80. 65

    65

    65

    Returns: 65

  81. 9

    9

    2

    Returns: 7

  82. 2

    3

    30

    Returns: 12

  83. 5

    3

    3

    Returns: 4

  84. 62

    62

    62

    Returns: 62

  85. 10

    10

    10

    Returns: 10

  86. 3

    2

    3

    Returns: 3

  87. 3

    5

    3

    Returns: 4

  88. 7

    7

    6

    Returns: 7

  89. 5

    5

    4

    Returns: 5

  90. 2

    1

    1

    Returns: 2

  91. 99

    100

    100

    Returns: 100

  92. 9

    10

    10

    Returns: 10

  93. 4

    4

    3

    Returns: 4

  94. 12

    13

    13

    Returns: 13

  95. 5

    1

    2

    Returns: 3

  96. 5

    6

    6

    Returns: 6

  97. 2

    2

    1

    Returns: 2

  98. 1

    3

    1

    Returns: 2

  99. 1

    1

    99

    Returns: 34

  100. 78

    53

    63

    Returns: 65

  101. 3

    5

    6

    Returns: 5

  102. 60

    61

    61

    Returns: 61

  103. 8

    8

    10

    Returns: 9

  104. 11

    11

    1

    Returns: 8

  105. 22

    45

    61

    Returns: 43

  106. 8

    8

    1

    Returns: 6

  107. 2

    1

    2

    Returns: 2

  108. 6

    4

    4

    Returns: 5

  109. 5

    2

    1

    Returns: 3

  110. 92

    90

    90

    Returns: 91

  111. 6

    7

    8

    Returns: 8

  112. 100

    89

    20

    Returns: 70

  113. 11

    3

    3

    Returns: 6

  114. 9

    9

    11

    Returns: 10

  115. 4

    3

    3

    Returns: 4

  116. 3

    4

    3

    Returns: 4

  117. 2

    1

    3

    Returns: 3

  118. 17

    19

    20

    Returns: 19

  119. 44

    44

    44

    Returns: 44

  120. 20

    20

    1

    Returns: 14

  121. 6

    2

    6

    Returns: 5

  122. 12

    11

    99

    Returns: 41

  123. 4

    3

    1

    Returns: 3

  124. 3

    6

    5

    Returns: 5

  125. 23

    98

    78

    Returns: 67

  126. 8

    6

    6

    Returns: 7

  127. 100

    100

    99

    Returns: 100

  128. 99

    3

    3

    Returns: 35

  129. 5

    7

    8

    Returns: 7

  130. 12

    12

    14

    Returns: 13

  131. 20

    30

    40

    Returns: 31

  132. 99

    96

    1

    Returns: 66

  133. 4

    3

    7

    Returns: 5


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