Name substitution path designer

Make the route part of the naming clue

A name can be the destination of a puzzle without being an anagram. The reader might have to cross a sequence of permitted labels, changing one position at a time. The intermediate forms then matter: a particular label can mark a required encounter, an unavailable tile can close a shortcut, and two equally short routes can support different discoveries.

This workbench designs that finite substitution exercise. You supply the forms, both endpoints, any ordered checkpoints and the move ceiling. It finds the shortest permitted walks, counts all of them and displays a bounded set of witnesses with exact changes. You can also submit a proposed route and see where it breaks the rules or takes unnecessary steps.

The model is deliberately explicit. One move changes one Unicode code point in the comparison form. It does not insert, delete or rearrange characters. First arrivals at required checkpoints follow the listed order. A form may be revisited after checkpoint progress, and the target cannot be entered before all checkpoints. This is a shortest-walk model; it does not certify a rule forbidding every repeated form. Put that distinction in the reader’s instructions before building a scene around it.

Original fictional scene: two paths across the same exhibit

The museum’s new exhibit used eight invented name tiles. Visitors began at LINA, had to touch LIRA, and finished at MORA. A conservator asked two siblings to prepare an example before the opening. One arranged LINA, LIRA, MIRA, MORA along the left edge of the table. The other laid out LINA, LIRA, LORA, MORA beside it.

The first sibling changed the third position, then the first, then the second. The second changed the third, then the second, then the first. Both had used three moves. The conservator had printed a small card saying “the shortest route” and left space underneath for one answer. There was not enough space for the two rows now waiting on the table.

Instead of choosing a sibling’s arrangement and hiding the other, the conservator changed the card. Visitors would be invited to find a shortest route and then look for another. Each sibling wrote a note about the order of changes used. The exhibit credited both arrangements, while the name tiles remained the same. The new invitation let a visitor who finished quickly keep investigating rather than assume that a different answer must be a mistake.

The museum, siblings, tile convention and incident are original fiction. The eight forms are authored puzzle material, not a historical naming tradition or a list of verified personal names. The mathematical count would not establish who invented an arrangement or whether someone copied it. Those facts belong to the story, not to a graph calculation.

Consider changing the final tile from MORA to MERA. The new form must first be added to the supplied pool; merely editing the target should produce a missing-form error. With MERA added, the LIRA requirement and a three-move ceiling, LINA → LIRA → MIRA → MERA is the sole shortest route in that revised pool. The second sibling’s former route no longer finishes the new task in three moves. That revision changes the exhibit’s invitation and how its two contributions can be shown. Use this counterfactual method to test whether a changed name alters the clue’s structure, rather than treating spelling revisions as decorative.

The supplied pool is the puzzle’s boundary

Enter two to six hundred distinct forms, one per line. Each has two to twenty-four Unicode code points and at most forty-eight UTF-16 units. Empty lines are ignored. Leading or trailing whitespace and control characters are rejected, so an accidental space cannot quietly become a secret move. Internal spaces and other permitted symbols remain part of the comparison.

The program does not decide whether an intermediate is an acceptable real word or name. A fictional cipher alphabet, an exhibit’s printed labels or an explicitly approved character-name pool can all provide the finite material. If you want attested forms, research and document that material separately. Large naming corpora elsewhere in the site do not make every item suitable for a reader’s puzzle, and theoretical combinations do not count as dictionary evidence.

Both endpoints must resolve to different listed forms with the same comparison length. Forms of other lengths remain visible in the scope report as exclusions. They do not become insertion or deletion moves. Blocked entries also stay visible in the private report; the reader sheet contains the eligible pool rather than suggesting those excluded forms are usable.

Exact comparison changes nothing. The optional ASCII policy converts A–Z to a–z only, preserving the original pool spelling beside the comparison form. It does not normalize Unicode, infer pronunciation, remove punctuation or transliterate. Two listed originals that collide under the chosen policy cause an explicit error. Choose a consistent representative or a different policy rather than silently merging the scope.

Read the change positions, not an imagined sound rule

Every witness step shows the original listed forms, comparison forms and the one-based position that changes. LINA → LIRA changes position three from N to R. LIRA → MIRA changes position one from L to M. MIRA → MORA changes position two from I to O. The endpoint difference is three positions, which supplies a lower bound of three substitutions.

That lower bound is not always attainable. The pool may lack a necessary intermediate, and required checkpoints can force a detour. An endpoint difference of three does not prove a three-move puzzle. Compare the bound with the actual shortest distance rather than treating it as an answer generator.

A code point is the declared counting unit, not necessarily a reader-perceived grapheme. An astral symbol can occupy one code point while using two UTF-16 units; a visible accented sequence can contain several code points. The tool follows its stated unit without claiming cultural or phonetic equivalence. If that unit is inappropriate for your audience, redesign the printed forms and instructions instead of describing the result as a pronunciation puzzle.

Under ASCII folding, a raw step can visibly differ in capitalization at additional positions even when its comparison forms differ at just one. That is why both columns remain available. The reader must receive the same policy. A private proof based on folded comparison cannot justify a handout that tells readers to compare raw capital letters exactly.

Checkpoints change the state, not just the introduction

You may specify up to six distinct required forms, in order. They must be listed, eligible and different from the endpoints. A future checkpoint cannot be entered before the current one, and the target is unavailable until all checkpoints have been reached. Revisiting a form after progress is allowed and is disclosed in the witness.

For a useful stress test, keep only LINA, LIRA, MINA, MONA and MORA. Require LIRA and raise the ceiling to five. The shortest walk becomes LINA → LIRA → LINA → MINA → MONA → MORA. LIRA is a dead end in that pool, so the walk returns to LINA after satisfying the checkpoint. The card explicitly lists that repeated form. Calling this a repeat-free ladder would misdescribe the implemented exercise.

The search therefore tracks a form together with how many checkpoints have been completed. Returning to LINA after LIRA is a different progress state from the initial LINA. With at most six checkpoints, the finite state bound is the number of eligible forms multiplied by seven. The report exposes the visited-state count and its bound rather than pretending to explore every imaginable name.

Local substitutions connect both directions, but checkpoint progress makes the complete exercise directional. Do not assume that reversing a printed witness automatically creates a valid reversed puzzle. Prepare the new endpoints and checkpoint order explicitly, then run the revised scope. The tool checks the resulting rules rather than relying on the appearance of a reversible arrow.

Separate distance, route count and displayed examples

The engine computes the global shortest distance within the declared finite progress graph. If that distance is three and the ceiling is two, the report says that a route exists but exceeds the budget. It does not call the target unreachable. If no goal state is reachable at all, it reports that different conclusion, scoped to the supplied pool and checkpoint order.

All shortest walks are counted exactly and exported as a decimal string. The witness limit, from one to twelve, controls only how many routes are displayed. In the default pool, requiring LIRA leaves two shortest walks. Removing the checkpoint exposes six. Setting the sample limit to one does not turn either count into one or establish a unique route.

Only shortest walks are included in that count. Longer walks, especially when revisits are permitted, are a different set. The reader exercise asks for a shortest walk within the ceiling; it does not say that every route under a larger ceiling has been enumerated. A unique shortest route in this finite graph also says nothing about forms you never supplied.

Treat uniqueness as a design choice. Two shortest answers may be welcome when a scene rewards exploration, as in the exhibit. If the plot requires one exact sequence, inspect the alternatives and change a real constraint: remove an intermediate, require a checkpoint or revise an endpoint. Explain the revised rule to the reader. A hidden ban added only in the author’s proof would make the published exercise a different puzzle.

Validate a proposed walk without confusing it with the search

The optional route field accepts up to sixty-one forms. The validator checks the start, target, pool membership, length, blocked forms, each local substitution, checkpoint order and move ceiling. It then compares an otherwise legal route with the computed shortest distance. A valid longer walk is distinguished from an invalid step and from a shortest solution.

For example, LINA → MORA changes several positions at once and fails the local rule. LINA → LIRA → LINA → LIRA → MIRA → MORA can obey the substitution and checkpoint rules under a five-move ceiling, but it is longer than the three-move optimum in the full default pool. These are different failure explanations, with different remedies.

The witness controls place a currently displayed sample into the proposed-route field and rerun validation. If you edit the pool, policy, checkpoints, exclusions, ceiling or other puzzle source context first, an old visible control refuses to overwrite your route. Recompute and inspect the new witness. The attempt itself may be replaced intentionally; the button is not permission to apply an old solution to a changed puzzle.

An unsuccessful submitted route does not erase the independent existence proof. The puzzle can remain solvable while a particular attempt is wrong. No attempt supplied means no response was observed; the program does not invent a player, completion time or success rate. Use the findings to revise a concrete exercise, not to claim audience testing that never occurred.

Give the reader the exercise and keep the proof private

The reader download appears only when a witness fits the ceiling. It contains the authored prompt, both endpoints, eligible pool, ordered checkpoints, comparison policy, ceiling and explicit shortest-walk rules. It omits witness paths, shortest counts, submitted attempts and the private story-purpose field. Both endpoints are intentionally visible: this is not a certificate for the fairness of an unstated identity riddle.

Your authored prompt is included verbatim. Check it for an answer sequence or a spoiler you accidentally pasted there; the software does not infer and redact the meaning of your own instructions.

The private audit remains available for a valid scope even when no route fits. It retains excluded forms, constraints, the proposed attempt and the actual conclusion. Private proof exports, copying, favorites and comparison retain solution information and your story notes. A saved project restores the editable design; it is not a reader-safe handout. Inspect the appropriate file before sharing it.

Anagrams ask whether a character inventory can be rearranged. Ordered extraction clues ask which positions or rows yield a hidden form. This task asks whether legal intermediate substitutions connect two declared forms, and whether the shortest connection is unique in a finite scope. Choose the tool whose rule the reader can actually use, then make that rule visible in the story.

Is this an anagram checker with extra steps?

No. Anagrams compare character inventories. This tool requires every adjacent pair to substitute exactly one comparison code point and every intermediate to belong to the supplied eligible pool. Ordered checkpoint progress and shortest-walk counts are separate constraints.

Can I require that no form ever repeats?

This implementation allows revisits after checkpoint progress and exposes them. It does not certify repeat-free simple paths. Change the pool and checkpoint design if the printed puzzle needs a no-repeat rule, then inspect the resulting witnesses rather than mislabelling this model.

Why does one displayed witness still say six shortest walks?

The sample limit controls presentation only. The exact count covers all shortest walks in the declared state graph. Increase the sample cap to inspect more alternatives; do not call a single displayed route a unique answer.

Does the reader sheet automatically remove every spoiler?

It omits generated solutions, counts, attempts and the private note. Your authored public prompt is included literally, so inspect it for pasted answers or plot information. Both endpoints are intentionally shown, and the tool does not interpret your prose.