The Die Hard Water Jug Riddle (Solved)

This riddle is from famous Die Hard movie where Bruce Willis and Jackson have to diffuse a bomb by placing exactly 4 gallon water on a scale using 3 gallon and 5 gallon water jug.

Riddle

You have a 3-gallon and a 5-gallon jug that you can fill multiple times from a tap 🚰. The problem is to measure exactly 4 gallons of water.

How do you do it?

Think for a while before looking at the solution.

Solution

Firstly you will try to measure 4 gallons of water by estimation. For e.g. adding 3 gallons of water to 1/3 of the 3 gallon jug. But this riddle is asking for a precise measurement so this won’t work.

We can quick realize this:-

5 – 3 = 2 and 5 – (3 – 2) = 4

Here is one of the solution of this riddle:

Action	3-gallon jug	5-gallon jug
Fill up 5-gallon jug	-	5
Fill up 3-gallon jug with water from 5-gallon jug	3	2
Pour out 3-gallon jug	0	2
Transfer water from 5-gallon jug to 3-gallon jug	2	0
Fill up 5 gallon jug again	2	5
Transfer water from 5-gallon jug to 3-gallon jug	3	4

That’s not the only solution. There are multiple solutions possible for this riddle.

Incidentally, the reason we can find a solution is because the two numbers 5 and 3 are prime numbers (i.e. they have no common divisors). We can actually generate any volume of water from 1 to sum of these two prime numbers (i.e. 5 + 3 = 8) (in fact, we did get measurements of 2, 3, 4, 5 and 7 along the way in our solutions).

• We have measured 2 and 3 in 3-gallon jug along the way in our solution
• We have measured 4 and 5 in 5-gallon jug along the way in our solution
• We have measured 7 in last two actions summing up gallons in both jugs
• we can measure exactly 8-gallons by filling up both 5-gallon and 3-gallon jugs