Random Configurable Bingo Card Generator

Description

Generate a bounded integer bingo grid with explicit column ranges, column/card-wide uniqueness and an optional free cell using randomized augmenting-path matching; overlapping ranges are supported, search is bounded and cards are not uniform over all feasible layouts.

A generated practice exercise contains a prompt and an answer key under a specific rule set. A planted answer establishes one possible solution; only an explicit enumeration or uniqueness check establishes whether alternatives exist.

When to use this tool

Use this generator to create reproducible bingo card cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply rows, columnBounds, uniqueness, freeCell, maximumSearchSteps in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read board, uniqueNumbers, filledCellCount, searchSteps. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Build column-specific integer domains and assign values to all nonfree slots through randomized augmenting-path matching. Enforce uniqueness within columns or across the card, leaving the optional free cell null, and return used numbers and search steps.^[1]

Delegated operations used for this result: unique. Their calculation or parsing conventions apply to the corresponding result fields.^[2]

Input field	Meaning and units	Accepted input
rows	Rows	Required. Safe integer; minimum 1; maximum 16.
columnBounds	Column Bounds	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 16.
columnBounds[].minimum	Minimum	Required. Safe integer.
columnBounds[].maximum	Maximum	Required. Safe integer.
uniqueness	Uniqueness	Required. Text; one of "column", "card".
freeCell	Free Cell	Optional. Object; no unknown keys.
freeCell.row	Row	Required. Safe integer; minimum 0; maximum 15.
freeCell.column	Column	Required. Safe integer; minimum 0; maximum 15.
maximumSearchSteps	Maximum Search Steps	Required. Safe integer; minimum 1; maximum 1000000.
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
board	Board	Required. Object; no unknown keys.
board.values	Values	Required. Array of Array of Safe integer. or Null.; minimum items 1; maximum items 16.; minimum items 1; maximum items 16.
board.freeCell	Free Cell	Required. Object; no unknown keys. or Null.
uniqueNumbers	Unique Numbers	Required. Array of Safe integer.; maximum items 256.
filledCellCount	Filled Cell Count	Required. Safe integer; minimum 0; maximum 256.
searchSteps	Search Steps	Required. Safe integer; minimum 0; maximum 1000000.
randomness	Replay source and normalized 32-bit seed, or null seed for an advancing context source.	Required. Object; no unknown keys.
randomness.seed	Optional safe-integer replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "rows": 3,
    "columnBounds": [
      {
        "minimum": 1,
        "maximum": 5
      },
      {
        "minimum": 6,
        "maximum": 10
      },
      {
        "minimum": 11,
        "maximum": 15
      }
    ],
    "uniqueness": "card",
    "freeCell": {
      "row": 1,
      "column": 1
    },
    "maximumSearchSteps": 10000,
    "seed": 42
  },
  "output": {
    "board": {
      "values": [
        [
          5,
          9,
          13
        ],
        [
          3,
          null,
          14
        ],
        [
          1,
          7,
          11
        ]
      ],
      "freeCell": {
        "row": 1,
        "column": 1
      }
    },
    "uniqueNumbers": [
      1,
      3,
      5,
      7,
      9,
      11,
      13,
      14
    ],
    "filledCellCount": 8,
    "searchSteps": 24,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Overlapping column ranges can make card-wide matching infeasible even when each column has enough values. First-feasible matching is bounded and not uniform over valid cards; a generated card is not a gambling or prize system.
A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Configurable Bingo Card Generator — tool.io
Calculation or validation: list/unique — tool.io

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