Description
Hide selected cells in caller-provided, caller-verified formula/truth-table pairs and classify the answer column without parsing or evaluating the formula.
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.
Hide selected cells in caller-provided, caller-verified formula/truth-table pairs and classify the answer column without parsing or evaluating the formula.
When to use this tool
Use this generator to create reproducible truth table gap puzzle 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 variables, pairs, callerVerified, provenance, hiddenCount, 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 contentSource, variables, valuationOrder, valuations, cases, provenance. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Require caller-verified formula/column pairs covering every binary valuation. Draw a pair, hide distinct truth-table rows as null cells and delegate tautology, contradiction and contingency classification of the full answer column. Preserve false-first ascending binary valuation order with the first variable as the most significant bit.1
Delegated operations used for this result: tautology all true checker; contradiction all false checker. Their calculation or parsing conventions apply to the corresponding result fields.2, 3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| variables | Variables | Required. Array of Text; maximum UTF-16 length 32.; minimum items 0; maximum items 8. |
| pairs | Pairs | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 32. |
| pairs[].formula | Formula | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 256. |
| pairs[].values | Values | Required. Array of Boolean.; minimum items 1; maximum items 256. |
| callerVerified | Caller Verified | Required. Boolean; exactly true. |
| provenance | Provenance | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 512. |
| hiddenCount | Hidden Count | Required. Safe integer; minimum 0; maximum 256. |
| count | Requested count; the mechanics explain whether one draw expands into several returned records. | 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 |
|---|---|---|
| contentSource | Content Source | Required. Text; exactly "caller-provided". |
| variables | Variables | Required. Array of Text; maximum UTF-16 length 32.; minimum items 0; maximum items 8. |
| valuationOrder | Valuation Order | Required. Text; exactly "ascending-binary-false-first-msb". |
| valuations | Valuations | Required. Array of Array of Boolean.; minimum items 0; maximum items 8.; minimum items 1; maximum items 256. |
| cases | Cases | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 32. |
| cases[].puzzle | Puzzle | Required. Object; no unknown keys. |
| cases[].puzzle.formula | Formula | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 256. |
| cases[].puzzle.cells | Cells | Required. Array of Boolean. or Null.; minimum items 1; maximum items 256. |
| cases[].answer | Answer | Required. Object; no unknown keys. |
| cases[].answer.values | Values | Required. Array of Boolean.; minimum items 1; maximum items 256. |
| cases[].answer.classification | Classification | Required. Text; one of "tautology", "contradiction", "contingency". |
| cases[].answer.tautology | Tautology | Required. Boolean. |
| cases[].answer.contradiction | Contradiction | Required. Boolean. |
| provenance | Provenance | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 512. |
| 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": {
"variables": [
"p",
"q"
],
"pairs": [
{
"formula": "p || !p",
"values": [
true,
true,
true,
true
]
},
{
"formula": "p && q",
"values": [
false,
false,
false,
true
]
}
],
"callerVerified": true,
"provenance": "Caller-verified illustrative formula/table pairs",
"hiddenCount": 2,
"count": 1,
"seed": 42
},
"output": {
"contentSource": "caller-provided",
"variables": [
"p",
"q"
],
"valuationOrder": "ascending-binary-false-first-msb",
"valuations": [
[
false,
false
],
[
false,
true
],
[
true,
false
],
[
true,
true
]
],
"cases": [
{
"puzzle": {
"formula": "p && q",
"cells": [
false,
null,
null,
true
]
},
"answer": {
"values": [
false,
false,
false,
true
],
"classification": "contingency",
"tautology": false,
"contradiction": false
}
}
],
"provenance": "Caller-verified illustrative formula/table pairs",
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- The formula text is not parsed or evaluated. The supplied column must already match it, and hidden cells need not have a uniquely deducible completion from the visible cells alone.
- 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
- Random Integer Partition Matching Puzzle Generator
Construct bounded positive or nonnegative integer compositions and optional canonical unordered partitions, retaining exact sum and conventions.
- Random Nonogram Line Completion Puzzle Generator
Generate a binary Nonogram line with hidden cells and exact bounded completion counts and forced-cell answers.