 Solution

Use a Spreadsheet class owning a private rectangular Java array of cells. Each immutable internal Cell contains a private tag Kind with values EMPTY, LABEL, NUMBER, FORMULA, and the corresponding payload: a string, a double or a formula reference. The tag determines which payload is meaningful, and the spreadsheet's setters create valid combinations rather than letting callers change fields independently. The cell object need not be public; public methods can expose its kind and label when needed for display.

Provide public setEmpty(r,c), setLabel(r,c,text), setNumber(r,c,x) and setFormula(r,c,f) methods, each checking its target coordinates and invalidating cached results. A public valueAt(r,c) supplies the numerical value, treating out-of-grid, empty and label cells as zero, and a public recalculate() brings all valid formulas up to date. Keep cached numeric results and evaluation-state flags private; they are derived data rather than editable cell content.

Define a public Formula interface with double evaluate(Lookup values, int row, int column). Lookup supplies only valueAt(r,c), so a formula can read dependencies without needing direct access to cells or a mutation API. An immutable AddFormula stores four integer offsets, two row/column pairs. It evaluates the two coordinates relative to the formula's own position and returns their sum. New formula kinds implement the same interface, avoiding changes to the storage representation or a large central switch over all formula operations.

The private spreadsheet dependency evaluation mechanism provides the Lookup implementation, checks cycles and caches evaluated cells. Formula evaluation is required to be side-effect-free with fixed dependencies during a recalculation. This separates encapsulation in object-oriented programming from extension: callers can change a cell through public setters and add new formula implementations, while internal cell invariants and cached values remain protected. Use tagged cell contents, an extensible formula interface and spreadsheet-owned evaluation state.