Use this tool when you need to assemble reproducible practice cards from a supplied, validated scenario corpus. Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.

1. Prepare the seed and the exact inventory or scenario inputs described below. Keep units, reference edition, and sampling convention explicit.
2. Enter seed, count, withoutReplacement, candidateInputsJson, following the field table and calculation rules below, then run the tool.
3. Read result. Inspect the nested fields in the output table below and keep any missing evidence or selected indices visible.
4. Correct any input issues and run again. Before using a successful result, review its units, signs, evidence coverage, and stated model or reference assumptions.

Enter 1–128 dense candidateInputsJson strings, each a strict JSON object for the imported calculator. Each string is at most 8192 UTF-16 units, the corpus at most 131072, and nesting at most 16 levels; nonfinite numbers and prototype-control keys are rejected. Select candidate positions under the sampling rules, then validate every candidate, including undrawn ones, by invoking the imported calculator with a fixed random source of 0.5. Any invalid candidate fails the whole request. Invoke it again for selected candidates with the request’s advancing source, and return original inputs, actual answer objects, selected indices, and never-selected indices. Duplicate candidate texts or equal answers may occur at distinct positions.^{[2, 3, 4]}

Use a nonblank seed of at most 256 UTF-16 units and a safe-integer count from 1 to 64. By default the seed is hashed into a deterministic pseudorandom state; each run restarts that state, so identical full inputs and implementation reproduce the result. The SDK may provide context.random, which replaces the seeded source and advances across the request; the seed remains required. Every source value must be finite in [0,1), with a request limit of 100000 source calls. Draw an index as floor(U×remainingSize). With replacement draw from the full inventory each time; without replacement remove each chosen position from an ordered pool and reject counts exceeding the inventory size. Uniform-source draws are over positions, not necessarily distinct values. This is not secure randomness.

The imported modular-power helper accepts safe-integer base, nonnegative safe-integer exponent, and positive safe-integer modulus. It uses BigInt repeated squaring and a normalized remainder for negative bases.

Each result.exercises entry preserves its supplied input and imported answer object. Additional roundTripAnswer, secondaryAnswer, prompts, or derived quantities appear only where the mechanics above describe them. selectedCandidateIndices and unusedCandidateIndices refer to the original corpus positions, not answer values.

The default source is deterministic pseudorandomness, not an independently audited or secure draw. Replacement applies to inventory positions; distinct positions may render identically or yield equal answers. Review the supplied inventory or scenario domain independently before interpreting the sample. Each answer retains the imported calculator’s unit conventions and domain assumptions. Randomizing a supplied scenario does not broaden that calculator’s capabilities.

Missing required fields, unknown fields, wrong types, and violated calculation rules return input issues. Numeric values must be finite; nonfinite numeric outputs are rejected. Arrays must be dense, with no missing cells. Extremely large composite outputs are rejected.

For a related task, use Random Number Property Classification Exercise Generator: A Harshad-number test checks divisibility by the supplied integer’s decimal digit sum. Scenario cards retain that particular property rather than offering a general classification of every number property. For a complementary step, use Random Newton Step Exercise Generator: A damped Newton step uses a parameter, gradient, and nonzero Hessian under a local model. Sampling supplied cases demonstrates that calculation without guaranteeing optimization convergence.

• Random Number Property Classification Exercise Generator

  A Harshad-number test checks divisibility by the supplied integer’s decimal digit sum. Scenario cards retain that particular property rather than offering a general classification of every number property.

• Random Newton Step Exercise Generator

  A damped Newton step uses a parameter, gradient, and nonzero Hessian under a local model. Sampling supplied cases demonstrates that calculation without guaranteeing optimization convergence.