Partition Combinations

We have a set of digits:
[6, 8, 4, 5, 2, 3]
Our goal is to partition these digits into two groups so that the difference between their sums is minimized.
Let's explore several possible partitions and find the optimal solution.
Partition 1: [6, 8, 4] and [5, 2, 3] → Sums: 18 and 10 → Difference: 8
Partition 2: [6, 5, 2] and [8, 4, 3] → Sums: 13 and 15 → Difference: 2
Partition 3: [6, 3, 5] and [8, 4, 2] → Sums: 14 and 14 → Difference: 0
Partition 4: [6, 8, 2] and [4, 5, 3] → Sums: 16 and 12 → Difference: 4
Partition 5: [6, 4, 3] and [8, 5, 2] → Sums: 13 and 15 → Difference: 2

Optimal Solution Analysis

After examining different partitions, we found that the optimal solution is:

Group 1: [6, 3, 5] = 14
Group 2: [8, 4, 2] = 14
Difference: 0 (Perfect balance!)

This partition is optimal because:

  • The sums of both groups are exactly equal (14)
  • Therefore, the difference between them is 0, which is the minimum possible
  • This creates a perfectly balanced partition

Other partitions like [6, 5, 2] and [8, 4, 3] were close with a difference of 2, but not perfect.