Two-jug measuring puzzle: rules and printable materials

Reach exactly four units in a five-unit jug using only full fills, full empties and complete pours. No real water is needed.

Players

1–6 cooperative

Plan for

10–15 minutes

Bring

Two drawn jugs of capacities 3 and 5, pencil

Use paper instead of water

Label two drawn containers A, capacity three, and B, capacity five. Start with both empty: (0,0). A state always records (amount in A, amount in B), in that order. The target is exactly four in B, regardless of A. Use a pencil and the printed state table; no actual containers, liquid, scale or running tap are required.

Allow only complete actions

One move fills either jug completely from an unlimited source, empties either jug completely, or pours from one into the other until the source is empty or the destination is full. Stop at the first of those two limits. You cannot stop halfway by judging a level, discard just one unit, change capacities or use a third vessel. Record both new amounts after each action.

Try a single legal example

From (0,5), pouring B into A gives (3,2): A fills after taking three units and B retains two. It does not give (2,3), because that would require stopping the pour early. From (3,4), pouring A into B gives (2,5); only one unit fits. These examples also show why the maximum pour equals the smaller of the source amount and available destination space.

Check success together

The separate host key gives a six-move solution from the empty start. Compare every row, including the starting row, rather than just the final four. If a proposed move is illegal, keep the previous valid state and choose again. A recorder may write while another participant chooses actions. There is no timer by default; the group succeeds when it can explain a valid path.

Change one constraint

After solving, ask whether capacities two and four could produce an odd amount; all reachable amounts stay even. This is a discussion prompt, not permission to change the original puzzle midway. A simpler first round uses capacities two and three with a target of one. State each new capacity and target before starting, and create a fresh key instead of reusing the printed four-unit answer.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.