Description
Generate a positive-target KenKen cage question and every valid hidden-cell replacement using cage arithmetic only, without global Latin-square constraints.
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 a positive-target KenKen cage question and every valid hidden-cell replacement using cage arithmetic only, without global Latin-square constraints.
When to use this tool
Use this generator to create reproducible kenken cage arithmetic quiz 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 gridOrder, cellCount, operation 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 puzzle, answer. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Draw cage values, derive the selected arithmetic target, hide one cell as zero, and delegate target checking. Enumerate every replacement from one through gridOrder that restores the target, returning all valid replacements separately.1
Delegated operations used for this result: kenken cage target product sum validator. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| gridOrder | Grid Order | Required. Safe integer; minimum 1; maximum 16. |
| cellCount | Cell Count | Required. Safe integer; minimum 1; maximum 8. |
| operation | Operation | Required. Text; one of "sum", "product", "difference", "quotient", "single". |
| 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 |
|---|---|---|
| puzzle | Puzzle | Required. Object; no unknown keys. |
| puzzle.operation | Operation | Required. Text; one of "sum", "product", "difference", "quotient", "single". |
| puzzle.target | Target | Required. Finite number. |
| puzzle.cells | Cells | Required. Array of Safe integer.; minimum items 0; maximum items 8. |
| puzzle.hiddenIndex | Hidden Index | Required. Safe integer. |
| answer | Answer | Required. Object; no unknown keys. |
| answer.values | Values | Required. Array of Safe integer.; minimum items 0; maximum items 8. |
| answer.replacementValues | Replacement Values | Required. Array of Safe integer.; minimum items 0; maximum items 16. |
| answer.targetMatches | Target Matches | Required. Boolean. |
| 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": {
"gridOrder": 6,
"cellCount": 2,
"operation": "product",
"seed": 42
},
"output": {
"puzzle": {
"operation": "product",
"target": 12,
"cells": [
4,
0
],
"hiddenIndex": 1
},
"answer": {
"values": [
4,
3
],
"replacementValues": [
3
],
"targetMatches": true
},
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- Single requires one cell and difference or quotient two; quotient targets can be fractional. The exercise does not construct a Latin grid or enforce row/column uniqueness, and a hidden cell can have multiple valid answers.
- 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
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