Logic Grid Puzzle Generator

Introduction:

A logic grid turns a short story into one-to-one relationships. If three people each chose a different room and a different object, every person must pair with exactly one room and one object. Solving means combining confirmed matches with exclusions until only one complete assignment remains.

The grid records that deduction without asking the solver to remember every consequence. A confirmed pairing marks one cell and rules out the rest of its row and column. An exclusion removes one candidate. Repeating those consequences across category pairs reveals facts that no single clue states outright.

Equal category sizes are essential. A three-item person category cannot participate in the same one-to-one model as a four-item room category because at least one item would have no partner or one partner would need to repeat. Three or four categories with three or four items each keep the worksheet readable and the complete assignment space bounded.

Difficulty can change how many clues a solver receives without changing the number of possible assignments before clues are applied. More direct or exclusion clues usually make a worksheet easier, while a shorter clue set asks the solver to derive more consequences. Wording can change the tone for a mystery or classroom handout, but it should never change the underlying relation.

A fair generated puzzle needs one answer, not merely an attractive grid. A seed makes the hidden assignment and clue order repeatable, while a solver count checks how many complete assignments satisfy every relation. Keep the seed with the answer key so the exact worksheet can be recreated.

How to Use This Tool:

Define a balanced one-to-one problem first, then judge the clue set by its verified solution count.

1. Load a starter preset or enter 3 to 4 category lines using Category: item, item, item.
2. Give every category the same 3 or 4 unique items. If the warning names a mismatched category, add or remove items until every line has the same count.
3. Set a short title, choose easy, medium, or hard difficulty, and select plain, mystery, or classroom clue wording.
4. Enter a Seed to make the assignment and clue order repeatable. Use New only when a different version is wanted.
5. Open Advanced to add exclusion clues from 0% to 60% in 5-point steps or allow clues between category pairs that do not include the first category.
6. Confirm that the summary and Solver audit report Unique and one solution, then compare the printable Puzzle sheet with the Answer key.

Interpreting Results:

Unique means exactly one assignment satisfies every generated clue. No solution means the relations contradict one another, and Ambiguous means at least two assignments remain because counting stops once a second solution is found.

The search-space count describes candidate assignments before clues are applied. It measures puzzle shape, not human difficulty. Clue count and clue mix describe the printed evidence, but a worksheet with more clues can still feel harder if labels are unfamiliar or relations are awkwardly distributed.

Check the clue ledger for clear names and readable relations even when the solver reports one answer. Computational uniqueness cannot detect confusing category labels, culturally obscure references, or wording that a learner might reasonably interpret another way.

Technical Details:

The first category anchors the assignment. Its items stay in their entered order, while every later category is represented as a permutation of item positions. The seed rotates and may reverse those permutations to create a repeatable hidden answer.

Formula Core

With c categories and n items per category, each non-anchor category can take any of n factorial orders. The total anchored search space is:

The base direct-clue set confirms every anchor-to-category pairing, so its size is:

Three categories with three items produce 36 anchored assignments and 6 direct clues. Four categories with four items produce 13,824 assignments and 12 direct clues. These exact bounds match the accepted puzzle sizes.

Mechanism Core

Every direct clue asserts that two items occupy the same anchor subject. Every exclusion asserts that they do not. The solver enumerates permutations for the non-anchor categories and applies all clue relations to each complete assignment. It stops at two solutions because the only needed status distinction is none, exactly one, or more than one.

Duplicate items within one category are removed with a warning. Category names are compared without regard to letter case and must be unique. The title and seed are required and may be at most 80 characters; category text may be at most 4,000 characters.

Clue wording is a presentation transform only. Plain, mystery, and classroom voices all preserve the same equality or inequality relation, so changing voice alone does not alter the answer, counts, or search space.

Accuracy Notes:

The solver verifies the generated binary match and exclusion relations within the supported 3-by-3 through 4-by-4 shapes. It does not judge the educational suitability or factual plausibility of custom category content.

• A displayed solution count of 2 means two or more because enumeration stops at that threshold.
• Changing the seed, category order, item order, difficulty, exclusion mix, or cross-category setting can change the puzzle.
• Short labels improve printed grid readability; uniqueness does not prevent visual crowding.

Worked Examples: