Examples
Examples
Try the starting example
- Train lengths (millimetres)
- 800,1000,1200
- Cassette usable lengths (millimetres)
- 900,1100
- Available rack slots (count)
- 2
- Train cassette assignments (JSON)
- [1,2,null]
- Rack-limited unassigned trains (count)
- 1
Try another scenario
- Train lengths (millimetres)
- 700,900,1100
- Cassette usable lengths (millimetres)
- 800,1000,1200
- Available rack slots (count)
- 3
- Train cassette assignments (JSON)
- [1,2,3]
- Rack-limited unassigned trains (count)
- 0
Calculation method
Calculation method
Train cassette assignments (JSON)
Match trains to cassette slots whose usable length>=train length; maximum-cardinality matching.
Rack-limited unassigned trains (count)
Count unmatched trains after limiting usable cassettes to first rack-slot count.
Symbols and units
- a
- Train lengths (millimetres)
- b
- Cassette usable lengths (millimetres)
- c
- Available rack slots (count)
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
- One train per cassette; all cassettes occupy one user-measured rack slot. No overhang allowed. Supported limits: All numeric inputs and computed intermediates must remain finite. Supported numeric input magnitude is zero or 1e-12 through 1e12 in absolute value; reject values outside this bounded range. All lists/JSON record tables are limited to 100 records unless a stricter bound is stated; reject malformed record arity and wrong member types. Positive train/cassette lengths; cassette list represents distinct physical cassettes; first rack-slot-count cassettes are available.
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.