Water Jug Puzzle Answer: Measure 4 Litres [Solved]

Water jug puzzle answer: fill the 5 litre jug, pour water into the 3 litre jug, empty the small jug, move the 2 litres left in the big jug into the small jug, refill the big jug, and top up the small jug. Exactly 4 litres stay in the big jug. The whole method takes 6 steps, and every step uses only filling, emptying, or pouring. No guessing, no markings, and no third container are needed.

The water jug puzzle answer below works because 5 minus 3 leaves 2, and that 2 litres becomes the key that unlocks 4. Once you see that first subtraction, the rest of the puzzle falls into place. This version is reported as an IHS Markit interview question on Glassdoor, where candidates were asked how to measure 4 litres with a 3 litre and a 5 litre canister. The question is used in interviews because it separates candidates who pour at random from candidates who track the state of both jugs.

Water Jug Puzzle Answer in 6 Steps

Start with both jugs empty. You have an unlimited tap, and you can fill a jug, empty a jug, or pour from one jug into the other until the source jug is empty or the receiving jug is full. Those are the only moves allowed.

Step	What you do	5 litre jug	3 litre jug
1	Fill the 5 litre jug from the tap	5 litres	0 litres
2	Pour from the 5 litre jug into the 3 litre jug until the small jug is full	2 litres	3 litres
3	Empty the 3 litre jug	2 litres	0 litres
4	Pour the 2 litres from the big jug into the small jug	0 litres	2 litres
5	Fill the 5 litre jug from the tap again	5 litres	2 litres
6	Pour from the 5 litre jug into the small jug until it is full	4 litres	3 litres

Step 6 is the finish. The small jug already holds 2 litres, so it can take only 1 more litre. That 1 litre leaves the big jug, and 5 minus 1 leaves exactly 4 litres in the big jug. Stop there. You have measured 4 litres, and you did it without ever estimating a level by eye.

Why the Water Jug Puzzle Answer Works

The puzzle is really a subtraction puzzle in disguise. Filling the big jug and pouring into the small jug is the physical version of 5 minus 3 equals 2. That 2 litres is a new, exact amount that neither jug could hold on its own at the start. Moving it into the small jug leaves exactly 1 litre of free space, and that free space is what turns a fresh 5 litres into 4 litres.

There is a simple test for whether a target like this is possible at all. Find the greatest common divisor of the two jug sizes. Here the sizes are 3 and 5, and their greatest common divisor is 1. Any whole number of litres up to the combined capacity of 8 litres can be measured when that divisor is 1. If the divisor did not divide the target, the puzzle would be impossible. For example, with a 4 litre jug and a 6 litre jug, you could never measure exactly 5 litres, because every amount you can make is a multiple of 2.

The Second Route to 4 Litres

The 6 step route above is the shortest, but it is not the only route. You can also start from the small jug. Fill the 3 litre jug, pour it into the big jug, fill the small jug again, and pour into the big jug until it is full. That leaves 1 litre in the small jug. Empty the big jug, move that 1 litre into it, fill the small jug, and pour all 3 litres in. The big jug then holds 1 plus 3, which is 4 litres.

This second route takes 8 steps, so present the 6 step version first in an interview. Both routes create a useful intermediate amount, 2 litres in the short route and 1 litre in the long route, and then add a full small jug to it.

The Trap Most Candidates Fall Into

The most common wrong answer is to measure 2 litres twice and add them together. On paper, 2 plus 2 equals 4, so it looks correct. In the puzzle as stated, it fails, because there is nowhere to store the first 2 litres while you measure the second batch. You have only the two jugs and the tap. Pouring the first 2 litres back into the tap, or into an imaginary third container, breaks the rules of the puzzle.

The second trap is estimating. A candidate who says they will fill the big jug to about four fifths of its height has not measured anything. Interviewers reject that answer at once, because the jugs have no markings and the whole point of the puzzle is exactness. Every amount in a correct answer must come from a jug being completely full, completely empty, or filled to the top by pouring.

The third trap is losing track of the state. Candidates who pour without writing down the two numbers after each step soon forget whether the small jug holds 2 litres or 1 litre. In the interview room, say the pair of numbers out loud after each move, just as the table above does. That habit turns a confusing puzzle into a short, checkable sequence.

What the Interviewer Is Testing in the Water Jug Puzzle Answer

First, the interviewer is testing whether you can model a problem with states. Each step changes only two numbers, the amount in each jug, and a strong candidate keeps those numbers visible at all times. Second, the interviewer is testing whether you work backwards from the target. The last step needs 1 litre of free space, so a good candidate asks what creates that space, and the answer is 2 litres sitting in the small jug.

Third, the interviewer is testing how you handle a constraint. The no markings rule and the two jug limit are not there to make life hard for no reason. They force you to use full and empty as your only measuring tools, which is exactly the skill behind resource allocation, capacity planning, and scheduling work. A candidate who tries to dodge the constraint has missed the point of the question.

Finally, the interviewer is listening to how you explain. A clear answer names the key insight early, walks through the steps without backtracking, and checks the final number. Saying “5 minus 3 is 2, and 2 leaves 1 litre of space, so 5 minus 1 is 4” in the first minute tells the interviewer that you have the structure, even before you list all 6 steps.

Try These Variations Next

Once the 3 litre and 5 litre version is clear, test yourself with new sizes. With a 4 litre jug and a 9 litre jug, can you measure exactly 6 litres? With a 3 litre jug and a 7 litre jug, can you measure exactly 5 litres? Apply the same test first. Check the greatest common divisor, check that the target is within the combined capacity, and then look for the small building block that leaves the right amount of free space.

Frequently Asked Questions

Can you measure 4 litres with a 3 litre and a 5 litre jug?

Yes. Fill the 5 litre jug, pour into the 3 litre jug to leave 2 litres, empty the small jug, move the 2 litres into it, refill the big jug, and top up the small jug. Exactly 4 litres remain in the big jug.

How many steps does the shortest solution take?

The shortest solution takes 6 steps. The alternative route starting from the small jug takes 8 steps, so present the 6 step version in an interview.

Why can you not just fill the big jug part way?

The jugs have no markings, so a part filled jug cannot be trusted as an exact amount. Every amount in a correct solution must come from a jug that is full, empty, or filled to the top by pouring.

Is this puzzle really asked in interviews?

Yes. Candidate reports on Glassdoor describe the 3 litre and 5 litre version being asked at IHS Markit, and the same puzzle appears in coding interview lists as the classic water jug problem. The wording varies, but the jugs and the target stay the same.

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