Examples
Examples
Try the starting example
- Items: name, weight kg, group that may share a box
- A,4,glass B,3,glass C,2,books D,1,books
- Available identical boxes
- 3
- Supplied maximum per box (kg)
- 5
- Box assignments
- Box 1: A; Box 2: B; Box 3: C + D
- Box loads including empty boxes (kg)
- 4, 3, 3
- Items left unassigned
- None
- Total packed weight (kg)
- 10
- Largest packed box load (kg)
- 4
Try another scenario
- Items: name, weight kg, group that may share a box
- A,4,glass B,3,glass C,2,books D,1,books
- Available identical boxes
- 2
- Supplied maximum per box (kg)
- 5
- Box assignments
- Box 1: A; Box 2: B
- Box loads including empty boxes (kg)
- 4, 3
- Items left unassigned
- C, D
- Total packed weight (kg)
- 7
- Largest packed box load (kg)
- 4
Calculation method
Calculation method
Box assignments
Sort heaviest first; choose the least-loaded box with the same group or no contents and enough remaining capacity. Box index breaks ties.
Box loads including empty boxes (kg)
Sum assigned item weights in each box, preserving available box order.
Items left unassigned
Items the declared greedy rule cannot fit. Different group labels never mix.
Total packed weight (kg)
Sum packed item weights.
Largest packed box load (kg)
Maximum resulting box mass; box tare is excluded.
Symbols and units
- a
- Items: name, weight kg, group that may share a box
- b
- Available identical boxes
- c
- Supplied maximum per box (kg)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- A group-separated weight-balancing heuristic with finite boxes. It excludes item volume, cushioning, box tare and material-strength validation. Unassigned items are reported; a heuristic miss does not prove that no other arrangement works.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: arithmetic and geometry ↗
Background reading; this does not imply endorsement or independent review of SumFizz.