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You are watching: 3 gallon jug and 5 gallon jug riddle

Posted February 4, 2013 by Presh Talwalkar. Read about me, or email me.

This is a difficulty that is prominently featured in the film Die hard With a Vengeance.

You have actually a 3-gallon and also a 5-gallon jug that you deserve to fill indigenous a fractional of water.

The difficulty is to fill one of the jugs v exactly 4 gallons of water. Exactly how do you do it?

Video: Die hard 3 The Water Jug math Riddle

. ."All will be fine if you usage your mind for your decisions, and mind just your decisions." because 2007, i have devoted my life to share the happiness of video game theory and mathematics. Keolistravelservices.com now has actually over 1,000 cost-free articles v no ads many thanks to community support! aid out and also get early access to articles with a pledge on Patreon.

. . . . . . M ns N D . Y O U R . D E C ns S i O N S . W E E K together Y . P U Z Z together E . . . . Answer come the water jug riddle

Math In Movies: The Water Jug Riddle indigenous Die hard With A Vengeance (1995)

The an initial attempt world have is to shot and estimate 4 gallons by including 3 gallons the water come 1/3 the the 3 gallon jug. But the riddle is asking for a specific measurement and so this solution cannot work.

The cheat is to establish that:

5 – 3 = 2 and 5 – (3 – 2) = 4

Here is one means to find the answer:


Incidentally, the reason we can find a solution is due to the fact that the 2 numbers 5 and also 3 are reasonably prime–that is, they have no common divisors. We can actually generate any kind of volume of water from 1 to 5 (in fact, us did get measurements of 1, 2, 3, 4, and also 5 along the means in our solutions).

The more general problem is recognize integer services for the equation ax + by = c. Remedies (x,y) exist when the greatest usual divisor the a and also b is a aspect of c. This is an ancient problem. Because that more, review this article: http://mathforum.org/library/drmath/view/51595.html ——————————————————— (This is the solution in level text)

1. To fill up the 5-gallon jug 2. Fill up the 3-gallon jug making use of the water from the 5-gallon jug (leaving 2 gallons in the 5-gallon jug) 3. Pour the end the 3-gallon jug right into the spring 4. Deliver the 2 gallons from the 5-gallon jug into the 3-gallon jug 5. Fill up the 5-gallon jug 6. Carry water native the 5-gallon jug till the 3-gallon jug is full. Due to the fact that the 3-gallon jug currently had 2 gallons that water, over there is room for just 1 gallon. 7. The quantity of water in the 5-gallon jug is precisely 4 gallons

If we signify the contents of the jugs as the pair (5-gallon jug amount, 3-gallon jug amount), the sequence of events is:

(5, 0)–>(2, 3)–>(2, 0)–>(0, 2)–>(5, 2)–>(4, 3)

That’s no the only path. Us can also consider the route:

1. Fill up the 3-gallon jug 2. Transport to the 5-gallon jug 3. Fill up the 3-gallon jug again 4. Transport water to fill up the 5-gallon jug, leaving 1 gallon in the 3-gallon jug 5. Empty the end the 5-gallon jug 6. Deliver the 1 gallon to the 5-gallon jug 7. To fill up the 3-gallon jug and also transfer the to the 5-gallon jug 8. The 5-gallon jug has 4 gallons of water

The sequence here is:

(0, 3)–>(3, 0)–>(3, 3)–>(5, 1)–>(0, 1)–>(1, 0)–>(1, 3)–>(4,0)


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