Water Jug puzzle online
Measure an exact amount with unmarked jugs. You may fill a jug completely, empty it completely, or pour from one jug into another until the source is empty or the destination is full. That tiny rule set creates a surprisingly rich planning puzzle because you never get to stop a pour halfway.
What makes this version different
Many water-jug pages show one famous example and then reveal the answer. This specialist is designed for repeat practice instead. Every source is generated inside the project and then solved independently as a finite state graph. The number shown as Start par is not a suggestion and not the length of one route the generator happened to know. It is the real minimum number of legal operations from the starting state to the goal.
The same graph search is available while you play. Optimal remaining tells you the fewest operations still required from your current volumes. Detour overhead compares your moves so far plus that remaining minimum with the original par. If the overhead stays at zero, a par solve is still possible. If it rises, you know immediately that the route has become longer than optimal.
The only legal operations
| Operation | What happens | Why it matters |
|---|---|---|
| Fill | A chosen jug goes straight to its full capacity. | You cannot choose an intermediate amount. |
| Empty | A chosen jug goes straight to zero. | Resetting a jug may be necessary to create a useful remainder. |
| Pour | Water moves until the source empties or the destination fills. | The stopping amount is forced, which creates exact differences between capacities. |
Every operation costs one move. Pouring one litre or nine litres still counts as one operation because the decision is the same: choose a source and destination and let the transfer continue to its forced boundary.
Easy, Standard and Challenge
Easy uses two jugs and the classic goal: get the target amount in either jug. The frozen sources have exact pars of four, six or eight moves. These are good for learning the repeatable rhythm of fill, pour, empty and pour back.
Standard uses three jugs, begins empty and still accepts the target in any jug. The third capacity creates alternate routes and more branching, so simply repeating one two-jug recipe is not enough. Exact pars run from five through eight moves.
Challenge uses three jugs but highlights one required destination jug. Some boards also begin with a non-empty state. Reaching the right amount in the wrong jug does not finish the puzzle. These sources have verified pars from eight through twelve moves and are meant to reward backward planning.
A practical solving method
Start by reading the capacities and the target, then ask which differences look useful. If the target is smaller than a jug, think about what amount would have to remain after filling another jug. When a pour leaves a remainder, that remainder is often more valuable than the jug you just filled.
For two jugs, it is often useful to commit to one pouring direction for a few steps instead of improvising. Fill the source, pour into the destination, empty the destination when necessary, then keep transferring. The repeated remainders are closely related to the greatest common divisor of the capacities. You do not need to calculate a formal proof while playing, but noticing that structure makes the puzzle feel less random.
With three jugs, avoid treating the third container as merely extra storage. It can preserve a remainder while the other two reset, which changes the reachable state graph. On Challenge, work backward from the required destination: what previous amount in another jug could pour into it and stop at exactly the target?
How Verified Hint works
The hint is not a memorized step from a single stored solution. At the moment you ask, the game searches the current jug volumes again. It finds the exact minimum distance to the goal and applies one legal operation that lies on a shortest route from that state. That matters after a detour, because the best recovery move may be different from the move that belonged to the original optimal route.
Check uses the same principle without moving anything. It reports the exact number of optimal moves remaining and whether your current route can still finish on original par. Both tools mark the run Assisted because they expose solver information that a Clean solve would have to infer.
Controls and accessibility
Each jug has Fill and Empty buttons. You can also tap one jug and then another to pour, or use the direct A→B style pour buttons. Keyboard users can press 1–3 to select jugs, F to fill the focused jug, E to empty it and H for a hint. Undo and Redo let you explore without losing the board, and Pause locks jug input and solver tools while the timer is stopped.
The jug graphic always shows the exact numeric amount as text as well as water height, so the puzzle does not depend on estimating a visual fill line. Challenge explicitly labels the required destination jug.
Why the minimum is trustworthy
A puzzle state is simply the amount in each jug. With capacities such as 7, 9 and 16 litres, there are only a finite number of possible triples. The release verifier independently rebuilds every Fill, Empty and Pour transition and performs breadth-first search. It checks the frozen source metadata, every jug-order permutation, thousands of deterministic Practice starts and the full 2026 Daily calendar.
The current V0.134 bank contains 90 project-generated sources: 30 Easy, 30 Standard and 30 Challenge. Their jug-order permutations create 420 verified starting presentations. The state spaces are deliberately small enough that the browser can recompute a genuine shortest route during play instead of using an estimate.
Common mistakes
- Trying to pour a chosen amount: partial pours are not legal. A pour always continues to a boundary.
- Chasing the target too early: sometimes the useful move creates a remainder that only becomes the target two or three operations later.
- Emptying without a plan: an empty jug creates capacity, but it also destroys a measured remainder. Ask what the empty space is for.
- Ignoring the required jug on Challenge: the right amount in the wrong destination is only an intermediate state.
- Assuming any solution is efficient: watch Detour overhead if you want to improve from a working route to a shortest one.
Practice or Daily?
Practice gives unlimited deterministic boards and supports exact replay through the seed in the URL. Daily Water Jug is separate from the platform’s frozen Today’s 6 rotation. It uses one date-stable verified source-permutation per day and keeps its own local history and streak. That lets the specialist build a repeat habit without silently changing the main six-game Daily contract.