Random Integer Partition Matching Puzzle Generator

Description

Construct bounded positive or nonnegative integer compositions and optional canonical unordered partitions, retaining exact sum and conventions.

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.

Construct bounded positive or nonnegative integer compositions and optional canonical unordered partitions, retaining exact sum and conventions.

When to use this tool

Use this generator to create reproducible integer partition matching 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 target, partCount, minimumPart, order 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 parts, target, sum, order, minimumPart. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Sequentially draw each part while reserving minimumPart for all later parts, then assign the final residual. Sort only in unordered mode and return the exact sum and target.^[1]

Input field	Meaning and units	Accepted input
target	Target	Required. Safe integer; minimum 0; maximum 1000000.
partCount	Part Count	Required. Safe integer; minimum 1; maximum 16.
minimumPart	Minimum Part	Required. Safe integer; one of 0, 1.
order	Order	Required. Text; one of "ordered", "unordered".
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
parts	Parts	Required. Array of Safe integer.; minimum items 1; maximum items 16.
target	Target	Required. Safe integer.
sum	Sum	Required. Safe integer.
order	Order	Required. Text; one of "ordered", "unordered".
minimumPart	Minimum Part	Required. Safe integer.
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.

json

{
  "input": {
    "target": 10,
    "partCount": 3,
    "minimumPart": 1,
    "order": "unordered",
    "seed": 42
  },
  "output": {
    "parts": [
      2,
      3,
      5
    ],
    "target": 10,
    "sum": 10,
    "order": "unordered",
    "minimumPart": 1,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

The target must accommodate every minimum part. Sorting does not make partitions uniformly sampled, and ordered mode returns a composition rather than an unordered integer partition.
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

Tool behavior and example: Random Integer Partition Matching Puzzle Generator — tool.io

Similar or alternative tools

Random Nonogram Line Completion Puzzle Generator
Generate a binary Nonogram line with hidden cells and exact bounded completion counts and forced-cell answers.
Random Palindrome Construction Puzzle Generator
Sample an ASCII alphanumeric character bank or caller-supplied individually palindromic words, mirror units, hide distinct positions, and return a checker-verified completion. The checker ignores case and separators; the supplied completion need not be unique and word mode requires each word to be a palindrome.