Description
Draw a bounded Pascal row and hide one exact string coefficient while retaining its row/column answer key.
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.
Draw a bounded Pascal row and hide one exact string coefficient while retaining its row/column answer key.
When to use this tool
Use this generator to create reproducible pascal triangle missing entry 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 minimumRow, maximumRow 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 row, column, prompt, answer. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw a zero-based Pascal row, obtain its binomial coefficients from the existing calculator, and choose one column to replace with null in the prompt. Return the hidden coefficient separately as answer.1
Delegated operations used for this result: pascal row. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| minimumRow | Minimum Row | Required. Safe integer; minimum 0; maximum 64. |
| maximumRow | Maximum Row | Required. Safe integer; minimum 0; maximum 64. |
| 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 |
|---|---|---|
| row | Row | Required. Safe integer. |
| column | Column | Required. Safe integer. |
| prompt | Prompt | Required. Array of Text. or Null.; minimum items 1; maximum items 65. |
| answer | Answer | Required. Text; minimum UTF-16 length 1. |
| randomness | Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional numeric 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.
{
"input": {
"minimumRow": 3,
"maximumRow": 5,
"seed": 42
},
"output": {
"row": 4,
"column": 2,
"prompt": [
"1",
"4",
null,
"4",
"1"
],
"answer": "6",
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Null denotes the omitted coefficient, not a zero value. Row bounds follow the linked calculator's supported integer range; hiding one entry does not guarantee any particular difficulty.
- A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
- 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
Similar or alternative tools
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- Random Integer Partition Matching Puzzle Generator
Construct bounded positive or nonnegative integer compositions and optional canonical unordered partitions, retaining exact sum and conventions.