A 3 and a 5 actually can give you any number between 1 and 8

How did they manage to empty and fill the jugs so quickly?

“There should be two jugs. . .A five-gallon and a three-gallon. Fill one of the jugs with exactly four gallons of water. . .If you’re still alive in five minutes, we’ll speak.”

– Simon Gruber Die Hard With A Vengeance

Remember that scene in Die Hard With A Vengeance where Bruce Willis and Samuel L. Jackson need to use two jugs to get exactly four gallons? I love riddles. And watching this one, I never could figure it out.

Here’s the dialogue. See if you can see where they “skip a step.”

Willis: Obviously we can’t fill the three gallon jug with four gallons of water, right?

Jackson: Obviously.

Willis: Alright. I know. Here we go. We fill the three gallon jug exactly to the top, right? Now, we pour that three gallons into the five-gallon jug. Giving us exactly three gallons in the five-gallon jug, right?

Jackson: Right. Then what?

Willis: Now, take the three-gallon jug, fill that a third of the way up. . .

Jackson: No, no, no. He said be precise. Exactly four gallons.

. . .

Willis: I got it! I got it! Exactly two gallons in here, right?

Jackson: Right.

Willis: Leaving exactly one gallon of empty space, right?

Jackson: Yeah.

Willis: A full five gallons here, right?

Jackson: Right.

Willis: If you pour one gallon out of the five gallons into there we have exactly. . .

Both: . . .four gallons in there!

Okay. Fair enough. They had two gallons in the three-gallon jug. Then, it was pretty simple to pour one gallon out of the five-gallon and they are left with four gallons in the five-gallon jug.

What the movie never explained was how they got those two gallons into the three-gallon jug. You have to admit that’s kind of an important step. And they didn’t show it because it’s hard to do. (I’ll explain how they got that two gallons in there below.)

But, here’s the thing. With a three-gallon and a five-gallon jug you can measure any amount from 1 gallon to 8 gallons.

One Gallon

1. Fill Three-Gallon jug (3G)
2. Pour 3G into Five-Gallon jug (5G)
3. Refill 3G
4. Pour two gallons from 3G into 5G.
5. 3G now has exactly one gallon

Total amount needed: six total gallons

Two Gallons

1. Fill 5G
2. Pour three gallons from 5G into 3G
3. 5G now has exactly two gallons

Total amount needed: five total gallons

Three Gallons

1. Fill 3G

(Okay, it was obvious, but y’all would have complained if I skipped Three Gallons!)

Four Gallons

This is the Die Hard scenario. And it’s the toughest on the list.

1. Fill 5G
2. Pour three gallons from 5G into 3G
3. Dump out 3G
4. Pour remaining two gallons from 5G into 3G

It was at this point that Bruce Willis says, “There’s exactly two gallons in here, right?” Sure, Bruce, but you kind of skipped four important steps.

5. Fill 5G
6. Pour one gallon from 5G into 3G
7. 5G now has exactly four gallons

Total amount needed: ten gallons

Five Gallons

1. Fill 5G

(Again, including it for completeness)

Six Gallons

1. Fill 3G
2. Pour 3G into 5G
3. Refill 3G
4. Both 3G and 5G both now have three gallons for a total of six gallons.

Total amount needed: six gallons

Seven Gallons

1. Fill 5G
2. Pour three gallons from 5G into 3G
3. Empty 3G
4. Pour remaining two gallons from 5G into 3G
5. Fill 5G
6. 3G now has 2 gallons and 5G has five gallons for a total of seven gallons.

Total amount needed: ten gallons

Eight Gallons

1. Fill 3G
2. Fill 5G
3. Yeah, 3+5 is still 8

Total amount needed: eight gallons

I enjoy riddles, but the first time I watched Die Hard With A Vengeance I spent the second half of the movie trying to figure out the riddle.

Note to directors, don’t give us riddles without giving us the solution! Especially when getting the riddle wrong means you die. I mean, what if that situation came up in real life and we were stuck wondering, “How did they get exactly two gallons in there?”

What movie riddles have made you think?

Stay safe

Rodney M Bliss is an author, columnist and IT Consultant. His blog updates every weekday. He lives in Pleasant Grove, UT with his lovely wife, thirteen children and grandchildren. Order Miscellany II, an anthology including his latest short story, “The Mercy System” here

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