Random Fraction Ordering Card Set Generator

Description

Generate rational cards with reduced forms and stable exact BigInt cross-product ordering, retaining ties without floating-point truth labels.

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.

Generate rational cards with reduced forms and stable exact BigInt cross-product ordering, retaining ties without floating-point truth labels.

When to use this tool

Use this generator to create reproducible fraction ordering card set 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 count, maximumDenominator, minimumNumerator, maximumNumerator 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 cards, order, equalAdjacent. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Draw signed integer numerators and positive denominators, reduce each fraction using the greatest common factor, and sort original card indexes by exact BigInt cross-products with stable input-index ties. Report equality of neighboring sorted cards.^[1]

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

Input field	Meaning and units	Accepted input
count	Count	Required. Safe integer; minimum 2; maximum 16.
maximumDenominator	Maximum Denominator	Required. Safe integer; minimum 1; maximum 1000000.
minimumNumerator	Minimum Numerator	Required. Safe integer.
maximumNumerator	Maximum Numerator	Required. Safe integer.
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
cards	Cards	Required. Array of Object; no unknown keys.; minimum items 2; maximum items 16.
cards[].numerator	Numerator	Required. Safe integer.
cards[].denominator	Denominator	Required. Safe integer.
cards[].reducedNumerator	Reduced Numerator	Required. Safe integer.
cards[].reducedDenominator	Reduced Denominator	Required. Safe integer.
order	Order	Required. Array of Safe integer.; minimum items 2; maximum items 16.
equalAdjacent	Equal Adjacent	Required. Array of Boolean.; minimum items 1; maximum items 15.
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": {
    "count": 2,
    "maximumDenominator": 5,
    "minimumNumerator": -2,
    "maximumNumerator": 4,
    "seed": 42
  },
  "output": {
    "cards": [
      {
        "numerator": 1,
        "denominator": 4,
        "reducedNumerator": 1,
        "reducedDenominator": 4
      },
      {
        "numerator": 2,
        "denominator": 5,
        "reducedNumerator": 2,
        "reducedDenominator": 5
      }
    ],
    "order": [
      0,
      1
    ],
    "equalAdjacent": [
      false
    ],
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Equivalent fractions and repeated cards are allowed. Exact rational comparison avoids floating-point quotient ordering, but generated numerators and denominators must satisfy the tool's safe-integer bounds.
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 Fraction Ordering Card Set Generator — tool.io
Calculation or validation: number/greatest-common-factor — tool.io

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