1. Maths problem-solving with Bruce Willis and Samuel L. Jackson
Die Hard III
Maths problem-solving with Bruce Willis and Samuel L. Jackson

2. Please go to
to view a short clip from the 1995 movie “Die Hard III”, starring Bruce Willis and Samuel L. Jackson.

3. The Problem.
Using only a 5 gallon jug and a 3 gallon jug, pour exactly 4 gallons of water into one of the jugs.

4. Using only a 5 gallon jug and a 3 gallon jug, pour exactly 4 gallons of water into one of the jugs.
We can only pour water in to a jug or pour it out – meaning the only mathematical operations available to us are addition (+) and subtraction (-).

5. Using only a 5 gallon jug and a 3 gallon jug, pour exactly 4 gallons of water into one of the jugs.
We can only pour water in to a jug or pour it out – meaning the only mathematical operations available to us are addition (+) and subtraction (-).
The only numbers available to us (initially) are 5 and 3. Our choices are = 8, with both jugs full and nowhere to go, and 5 – 3 = 2, decanting 3 gallons out of the 5 gallon jug into the 3 gallon jug.

6. Using only a 5 gallon jug and a 3 gallon jug, pour exactly 4 gallons of water into one of the jugs.
We can only pour water in to a jug or pour it out – meaning the only mathematical operations available to us are addition (+) and subtraction (-).
Decanting 3 gallons out of the 5 gallon jug into the 3 gallon jug leaves 2 gallons in the 5 gallon jug. Our task is now to extract 4, using + and/or -, with the numbers 2, 3 and 5 to play with.

7. Using only a 5 gallon jug and a 3 gallon jug, pour exactly 4 gallons of water into one of the jugs.
Our task is now to extract 4, using + and/or -, with the numbers 2, 3 and 5 to play with.
5 – 3 = 2 (again), = 8, 5 – 2 = 3, = 7 and = 5 don’t seem to lead anywhere, but 3 – 2 = 1 looks promising.

8. Using only a 5 gallon jug and a 3 gallon jug, pour exactly 4 gallons of water into one of the jugs.
So far:
5 – 3 = 2 (fill the empty 3 gallon jug from the full 5 gallon jug, leaving 2 gallons in the 5 gallon jug)
3 – 2 = 1 (empty the 3 gallon jug and pour the 2 gallons from the 5 gallon jug into the 3 gallon jug, leaving 1 gallon of space)
We now have an extra number (i.e. 1) to play with and immediately note that 5 – 1 = 4 (the required result), so what do we do?

9. Using only a 5 gallon jug and a 3 gallon jug, pour exactly 4 gallons of water into one of the jugs.
5 – 3 = 2 (fill the empty 3 gallon jug from the full 5 gallon jug, leaving 2 gallons in the 5 gallon jug)
3 – 2 = 1 (empty the 3 gallon jug and pour the 2 gallons from the 5 gallon jug into the 3 gallon jug, leaving 1 gallon of space)
5 – 1 = 4 (fill the 5 gallon jug, then fill up the 3 gallon jug (containing 2 gallons of water) from the 5 gallon jug, leaving 4 gallons in the 5 gallon jug!)

10. References / Sources: