Random Faded Solution Practice Packet Generator

Description

Sample supplied problems with replacement and delegate each selected problem's worked-example fade schedule at its packet position. Return visible prefixes, hidden suffixes and complete caller-authored step keys, including repeated problems and zero-step independent exercises; app presentation and pedagogical validity are separate.

A workflow or scheduling fixture makes ordering, dependencies, capacity, and timing explicit. Returning both the constructed records and their checks helps consumers distinguish a valid arrangement from a simulated failure case.

When to use this tool

Use this generator to create reproducible faded solution practice packet 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 problems, count 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 exercises, independentProblemCount. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.

Sample supplied problems with replacement and compute a fading schedule for each distinct solution length. Use the exercise's global position to choose how many leading solution steps remain visible and retain hidden/full steps separately.^[1]

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

Input field	Meaning and units	Accepted input
problems	Problems	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 64.
problems[].id	Literal identifier used independently of display labels.	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
problems[].prompt	Prompt	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 2048.
problems[].solutionSteps	Solution Steps	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 1024.; minimum items 1; maximum items 32.
count	Count	Required. Safe integer; minimum 1; maximum 32.
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
exercises	Exercises	Required. Array of Object; no unknown keys.; minimum items 1; maximum items 32.
exercises[].problemId	Problem Id	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 128.
exercises[].prompt	Prompt	Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 2048.
exercises[].providedStepCount	Provided Step Count	Required. Safe integer; minimum 0; maximum 32.
exercises[].visibleSteps	Visible Steps	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 1024.; maximum items 32.
exercises[].hiddenSteps	Hidden Steps	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 1024.; maximum items 32.
exercises[].solutionSteps	Solution Steps	Required. Array of Text; minimum UTF-16 length 1; maximum UTF-16 length 1024.; minimum items 1; maximum items 32.
independentProblemCount	Independent Problem Count	Required. Safe integer; minimum 0; maximum 32.
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": {
    "problems": [
      {
        "id": "P1",
        "prompt": "Solve x + 2 = 5",
        "solutionSteps": [
          "Subtract 2 from both sides.",
          "x = 3"
        ]
      },
      {
        "id": "P2",
        "prompt": "Solve 2x = 8",
        "solutionSteps": [
          "Divide both sides by 2.",
          "x = 4"
        ]
      }
    ],
    "count": 4,
    "seed": 42
  },
  "output": {
    "exercises": [
      {
        "problemId": "P2",
        "prompt": "Solve 2x = 8",
        "providedStepCount": 2,
        "visibleSteps": [
          "Divide both sides by 2.",
          "x = 4"
        ],
        "hiddenSteps": [],
        "solutionSteps": [
          "Divide both sides by 2.",
          "x = 4"
        ]
      },
      {
        "problemId": "P1",
        "prompt": "Solve x + 2 = 5",
        "providedStepCount": 1,
        "visibleSteps": [
          "Subtract 2 from both sides."
        ],
        "hiddenSteps": [
          "x = 3"
        ],
        "solutionSteps": [
          "Subtract 2 from both sides.",
          "x = 3"
        ]
      },
      {
        "problemId": "P2",
        "prompt": "Solve 2x = 8",
        "providedStepCount": 0,
        "visibleSteps": [],
        "hiddenSteps": [
          "Divide both sides by 2.",
          "x = 4"
        ],
        "solutionSteps": [
          "Divide both sides by 2.",
          "x = 4"
        ]
      },
      {
        "problemId": "P2",
        "prompt": "Solve 2x = 8",
        "providedStepCount": 0,
        "visibleSteps": [],
        "hiddenSteps": [
          "Divide both sides by 2.",
          "x = 4"
        ],
        "solutionSteps": [
          "Divide both sides by 2.",
          "x = 4"
        ]
      }
    ],
    "independentProblemCount": 2,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Sampling does not verify that supplied solutions are correct. Zero provided steps denotes an independent problem. The full answers are included and should be kept separate from learner-facing prompts.
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 Faded Solution Practice Packet Generator — tool.io
Calculation or validation: pedagogy/worked-example-fading — tool.io

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