1. Bin packing First-fit algorithm

2. 1 2 3 6 2 3 5 3 A B C D E F 4 Each block will be fitted into the first bin that has room for it. Bin packing First-fit algorithm

3. A B C D E F 4 The first block fits into the first bin. 1 2 3 6 2 3 5 3 Bin packing First-fit algorithm

4. A B C D E F 4 The second block fits into the first bin. 1 2 3 6 2 3 5 3 Bin packing First-fit algorithm

5. A B C D E F 4 The third block will not fit in the first bin 1 2 3 6 2 3 5 3 2 But there is room in the second bin. Bin packing First-fit algorithm

6. The third bin is the first one the 5 will fit into. A B C D E F 4 1 2 6 3 5 3 2 3 5 5 Bin packing First-fit algorithm

7. The second bin has room for the 3. Bin packing First-fit algorithm A B C D E F 4 1 2 6 33 2 3 5 3

8. The fourth bin is the first one with room for the 2. Bin packing First-fit algorithm A B C D E F 4 1 2 6 33 2 3 5 22 2

9. The 3 also fits into the fourth bin. Bin packing First-fit algorithm A B C D E F 4 1 6 3 2 3 5 2 333 3

10. No room until the fifth bin for the 6. Bin packing First-fit algorithm A B C D E F 4 1 6 3 2 3 5 2 3 666 6

11. The 3 has to start a new bin Bin packing First-fit algorithm A B C D E F 4 1 2 3 5 2 3 6 3333 3 3 Total usage is 6 bins.

12. Bin Packing Examples of first-fit algorithm

13. Example 1 Pack the following items into bins of size 20: 11, 7, 3, 4, 3, 5, 1, 8, 9 How many bins are required?

14. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

15. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

16. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

17. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

18. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

19. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

20. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

21. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

22. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

23. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

24. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11

25. 11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size 20 7 5 3 8 3 9 4 1 Bins 11 We need 3 bins.

26. Example 2 Pack the following items into bins of size 20: 5, 8, 12, 4, 11, 17, 7, 9, 7 How many bins are required?

27. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

28. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

29. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

30. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

31. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

32. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

33. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

34. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

35. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

36. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

37. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

38. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5

39. 5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size 20 8 17 11 9 12 7 4 7 Bins 5 We need 5 bins.

40. Example 3 A wholesale greengrocer is packing the following items into crates that will carry 24 kg: ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181 How many crates will the greengrocer need?

41. Crates (24 kg) ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

42. Crates (24 kg) 9 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

43. Crates (24 kg) 9 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

44. Crates (24 kg) 9 kg, 6 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

45. Crates (24 kg) 9 kg, 6 kg, 6 kg, 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

46. Crates (24 kg) 9 kg, 6 kg, 6 kg 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

47. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

48. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

49. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

50. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 20 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

51. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

52. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 10 kg 20 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

53. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

54. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

55. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 6 kg 20 kg 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

56. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 6 kg 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

57. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

58. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 8 kg 20 kg 10 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

59. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 8 kg 10 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

60. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

61. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

62. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 5 kg 20 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

63. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 5 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

64. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

65. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

66. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

67. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

68. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg, 18 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

69. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg, 18 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

70. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg, 18 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

71. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg 18 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

72. Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg 18 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181 So the greengrocer needs 6 crates.

73. Example 4 Pack the following items into bins of size 16: 14, 2, 7, 3, 1, 9, 12, 4, 6 How many bins are required?

74. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

75. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

76. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

77. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

78. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

79. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

80. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

81. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

82. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

83. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

84. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

85. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

86. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14

87. 14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size 16 2 9 1 4 7 6 3 12 Bins 14 We need 4 bins.

88. Example 5 A music store is ordering musical instruments. They are packed into boxes and delivered by a lorry. Each box can hold 20 kg. InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12 How many boxes will be needed to deliver all the instruments?

89. Boxes (20 kg) InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

90. Boxes (20 kg) InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

91. Boxes (20 kg) 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

92. Boxes (20 kg) 15 kg, 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

93. Boxes (20 kg) 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

94. Boxes (20 kg) 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

95. Boxes (20 kg) 15 kg, 2 kg 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

96. Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

97. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 2 kg 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

98. Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

99. Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

100. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 7 kg 15 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

101. Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

102. Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

103. Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

104. Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

105. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

106. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

107. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

108. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

109. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

110. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

111. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

112. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

113. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

114. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

115. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

116. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

117. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

118. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

119. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

120. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

121. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

122. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

123. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 18 kg 4 kg, 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

124. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

125. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

126. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

127. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

128. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 1 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

129. Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 1 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12 5 boxes are needed.