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Lizely

Water Sort Puzzle

Sort a fixed three-color water puzzle with touch and full keyboard controls, transparent pour feedback, Undo, and a 10-move minimum independently verified by breadth-first search.

Privacy: your files never leave your device. All processing happens locally in your browser.

How to use

  1. 1.Choose a non-empty source tube, then choose an empty destination or a non-full tube whose top color matches the source top color.
  2. 2.Use the two empty tubes as workspace while keeping four units of amber, blue, and teal conserved; Undo reverses the most recent legal pour.
  3. 3.Finish with three full monochrome tubes and two empty tubes to earn exactly 1,000 points; the independently verified minimum is 10 pours.

About Water Sort Puzzle

Water Sort Puzzle turns the familiar colored-liquid sorting game into one compact, deterministic browser challenge. The board contains five labeled tubes. Three begin full, two begin empty, and each tube has capacity for four liquid units. Amber, blue, and teal each occur exactly four times. Your goal is to finish with one full monochrome tube for each color and two empty tubes. The letters A, B, and T remain visible inside the liquid layers, so the state never depends on color perception alone.

The core rules follow the cited sources. A tube behaves as a stack: only the color at the top is accessible. Choose a non-empty source, then choose a different destination. The destination must either be empty or have the same color on top, and it must have free capacity. A pour transfers the connected run of same-colored liquid at the source top. If the destination has less room than the run contains, only the amount that fits moves. The scholarly FUN 2022 paper formally describes these Water Sort mechanics, while the independent gameplay guide confirms the same destination rule, whole-run behavior, four-unit tube convention, and monochrome completion condition.

The fixed arrangement, controls, scoring, error threshold, and presentation are Lizely product choices. Tubes are encoded from bottom to top. Tube 1 begins amber, blue, teal, amber. Tube 2 begins teal, amber, blue, teal. Tube 3 begins blue, teal, amber, blue. Tubes 4 and 5 begin empty. This disclosure makes every test and claimed solution reproducible. Reloading the page does not silently generate an easier board, and no random seed or remote level service changes the answer.

Touch and mouse play use a direct two-step interaction. Select a tube containing liquid, then select a destination. The chosen source is visibly marked and exposed through accessible button state. Selecting it again cancels the choice without making a pour. A legal destination immediately receives the full movable top run, the move counter increases once, and the source selection clears. Every tube is a native button with a touch-friendly target. Its accessible label states the entire content from bottom to top.

Keyboard play covers the complete game. Left or Up Arrow moves the logical cursor to the previous tube, while Right or Down Arrow moves it to the next tube. Enter or Space activates the cursor tube. Number keys 1 through 5 activate a tube directly, allowing an entire solution without pointer input. U undoes the last legal pour, and R restarts the board. The shared double-Escape boss key swaps the puzzle for a neutral spreadsheet view; using the gesture again restores the same puzzle state.

Illegal attempts never mutate the liquid arrangement. Choosing an empty source, targeting a full tube, or targeting a different top color leaves every tube and the legal move count unchanged. The live feedback names the exact problem. The first illegal attempt is repairable: choose a legal source and destination and continue from the identical board. A second illegal attempt deadlocks that run until Restart. This two-error limit is clearly disclosed product behavior, not a rule asserted by the external references.

Undo reverses the most recent legal pour, restoring the exact earlier tube arrangement, move count, and mistake count recorded before that move. It cannot invent or remove liquid. Restart is broader: it restores all 12 units to the published starting tubes, clears selection and history, returns the cursor to Tube 1, and resets score, moves, mistakes, completion, and feedback. Once the puzzle is complete or deadlocked, the terminal state freezes. Tube activation, arrow selection, number shortcuts, and Undo cannot alter the result; Restart begins a fresh run.

Any legal route that reaches the solved condition earns exactly 1,000 points. The reward does not depend on speed or a hidden move penalty. The independently verified minimum is 10 pours, so the disclosed shortest route provides an optional efficiency target, but a longer legal completion receives the same score. This keeps the win condition understandable and avoids presenting a product score as a standardized measure of reasoning ability.

The production solver uses breadth-first search only as a verification utility, not as a hidden automatic player. It serializes the five labeled tubes, explores legal source-destination pairs in numeric order, and visits each labeled arrangement once. Because every edge represents one pour, the first solved arrangement reached by the queue has minimum depth. The deterministic first route is Tube 1 to 4, 2 to 1, 3 to 2, 3 to 4, 1 to 3, 2 to 1, 2 to 4, 3 to 2, 1 to 3, and 1 to 4.

Release tests do not accept that production search as its own proof. An independent oracle represents the colors as single letters, implements its own top-run and capacity operations, and runs a separate queue. It independently finds the same 10-pour route. A second exhaustive traversal reaches 2,721 labeled states, counts 12,792 directed legal transitions, and finds 60 solved labelings. Sixty is expected because the three named color tubes and two empty tube positions may be permuted across five labeled positions.

State invariants are checked after every move in the shortest route. The board always has five tubes, no tube exceeds four units, and amber, blue, and teal remain at exactly four units each. Legal pours conserve all 12 units. Invalid attempts preserve the serialized tube key. Completion requires every non-empty tube to be both full and monochrome; merely splitting one color across two partly filled tubes does not pass. Tests also prove exact scoring, Undo restoration, repair after one error, deadlock after two, terminal freezing, cursor wrapping, and clean Restart behavior.

Everything runs locally in the browser. No puzzle state, move history, score, or input is uploaded. No account is required, no paid API is contacted, and no new runtime dependency is used. The fixed board has a tiny bounded state space, so moves remain immediate on mobile hardware. Responsive five-column controls use shrink-safe labels and compact spacing to avoid horizontal page overflow at a 390-pixel viewport.

This puzzle is recreational entertainment. It is not an intelligence test, aptitude measure, classroom placement tool, psychological instrument, hiring screen, or health assessment. Familiarity with Water Sort patterns changes performance, Undo is deliberately available, and a key slip may count as an illegal attempt. For a first solve, protect at least one empty tube and look for a top color that can expose a useful match. If a move hides the only available workspace, use Undo before committing another pour.

Methodology & sources

Represent each of five capacity-four tubes as a bottom-to-top color array. A legal transition requires a non-empty source, a different destination with free capacity, and either an empty destination or a matching top color. Move the maximum prefix of the connected source-top run that fits, then assert that all three color inventories remain four. Serialize labeled tubes and run breadth-first search from the disclosed initial board; numeric source and destination ordering produces a deterministic first minimum route of 10 pours. Independently reproduce the transition rule with letter tokens, compare the minimum route, and exhaust the reachable graph to verify 2,721 labeled states, 12,792 directed legal moves, and 60 solved labelings. Runtime invalid attempts preserve tube state, one error remains repairable, two errors deadlock, Undo restores the previous legal snapshot, completion awards exactly 1,000, and terminal states remain frozen until Restart.

Frequently asked questions

What moves during one pour?
The connected run of the same color at the source top moves together. If the destination cannot hold the entire run, only the amount that fits moves.
Why was my pour rejected?
The source may be empty, the destination may be full, or the destination top color may differ. A rejected attempt changes no tube and does not increase the legal move count.
What is the shortest solution?
Independent breadth-first search proves that this disclosed fixed board needs at least 10 pours. One route is 1→4, 2→1, 3→2, 3→4, 1→3, 2→1, 2→4, 3→2, 1→3, 1→4.
Does the 1,000-point score measure intelligence?
No. The fixed reward, Undo, and two-error stop are Lizely game behavior. This familiar puzzle is entertainment, not a standardized intelligence, education, employment, health, or psychological assessment.

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