Water Jars: plan the remainder before pouring

Think in exact states

Water Jars has two containers and six actions, but no freehand measuring. Filling makes a jar full. Emptying drains it. Pouring stops only when the source empties or the receiving jar fills. To reason clearly, write a state as an ordered pair: amount in A, amount in B. The capacities are fixed, so the pair records everything that matters for the next action.

The target may be reached in either jar. You do not need to empty the other one at the finish. This matters because a successful final pour can leave useful water in both containers. Read the displayed goal before planning: a familiar sequence for a different target can be perfectly legal and still fail to solve the current challenge.

A seven-and-nine teaching route

Consider a Standard configuration with capacity seven in A, capacity nine in B and a target of four. Start at (0, 0). First fill B, giving (0, 9). Pour B into A until A is full: (7, 2). The difference between the capacities has produced a measured remainder of two. Empty A to reach (0, 2), then pour B into A, giving (2, 0).

Now fill B again, reaching (2, 9). A has room for only five more units, so pouring B into A leaves (7, 4). The target is in B after six accepted actions. Every transfer followed a container boundary; no action required stopping halfway. Your current New puzzle may have different capacities or a different goal, so treat this as a worked configuration rather than a universal button sequence.

Make the next remainder deliberate

Before pouring, ask two questions: how much is in the source, and how much room remains in the destination? The smaller quantity is exactly what moves. In the final teaching step, the source holds nine and the destination has five spaces left. Five moves, leaving four. This calculation is more reliable than watching the water illustration and estimating its height.

Repeated states reveal an unproductive loop. If you return to the same ordered pair with the same target, the available next actions are exactly the same as before. Continuing the same sequence will not uncover a new measurement. Undo lets you return to the earlier decision without counting the discarded branch as part of the current route.

Use the minimum as a benchmark

The displayed shortest length comes from checking legal states with breadth-first search. The challenge banks require at least six moves on Standard, ten on Hard and fourteen on Expert. That benchmark does not force you to reproduce a particular route: any legal sequence reaching the target finishes. Invalid or unchanged actions add no move. Restart empties the same configuration, while New puzzle selects from a finite bank. Try explaining the intended remainder before each action; that explanation transfers more readily than memorizing a sequence of button positions.