The challenge
You have an unmarked 4-litre jug and an unmarked 9-litre jug, plus unlimited water. How can you measure exactly 6 litres?
4-Litre and 9-Litre Water Jug Puzzle
Solve this medium logic challenge, then compare your reasoning with the hint, checked answer, verification, and variation.
Hint
Create a known remainder by repeatedly filling the smaller jug.
Reach the six-litre state
Jug states in order
- Use two 4-litre transfers from a full 9-litre jug to leave one litre behind.
- Move that one litre into the empty 4-litre jug and refill the 9-litre jug.
- Pour three litres into the smaller jug, leaving exactly six litres in the larger jug.
Replay every legal state
Track the states after each move: (0,9), (4,5), (0,5), (4,1), (1,0), (1,9), then (4,6), with the 4-litre jug listed first.
Fill the 9-litre jug. Pour into the 4-litre jug, then empty the 4-litre jug. Pour another 4 litres from the large jug into the small one. The large jug now holds 1 litre. Empty the small jug and move that 1 litre into it. Fill the 9-litre jug again, then top up the small jug with 3 litres. The large jug now contains exactly 6 litres.
Why direct capacity arithmetic stalls
Searching only for a direct combination of jug capacities misses the useful remainder created by repeated pours.
Useful remainders create new states
Useful measurements can be created as remainders, not only as direct capacities.
How confident were you?
Track both jugs after every move
Represent a state as the amount in each jug. The useful intermediate state is one litre in the smaller jug, because topping it up removes exactly three litres from a full 9-litre jug.
Find the five-litre state
Try to measure exactly five litres with the same jugs. Find the earliest state in the original solution that already contains the answer.
Study how to solve logic puzzles for the reusable method behind this challenge. Then explore the logic puzzles and deductive reasoning learning path for connected examples and practice.