Edexcel D1 2024 January — Question 6

Exam BoardEdexcel
ModuleD1 (Decision Mathematics 1)
Year2024
SessionJanuary
TopicCombinations & Selection

6. The twelve numbers in the list below are to be packed into bins of size \(n\), where \(n\) is a positive integer.
28315251635182211271513
When the first-fit bin packing algorithm is applied to the list, the following allocation is obtained. Bin 1: 28315
Bin 2: 25161811
Bin 3: 352215
Bin 4: 2713
  1. Based on the packing shown above, determine the possible values of \(n\). You must give reasons for your answer.
  2. The original list of twelve numbers is to be sorted into ascending order. Use a quick sort to obtain the sorted list. You should show the result of each pass and identify your pivots clearly. When the first-fit decreasing bin packing algorithm is applied to the list, the following allocation is obtained. Bin 1: 35315
    Bin 2: 282716
    Bin 3: 252218
    Bin 4: 151311
  3. Determine the value of \(n\). You must give a reason for your answer.