Given three jugs with
pints in the first,
in the second, and
in the third, obtain a desired amount in one of the vessels by completely filling
up and/or emptying vessels into others. This problem can be solved with the aid of
trilinear coordinates (Tweedie 1939).

A variant of this problem asks to obtain a fixed quantity of liquid using only two initially empty buckets of capacities and and a well containing an inexhaustible supply of water.

This two bucket variant is used in the film Die Hard: With a Vengeance (1995). The characters John McClane and Zeus Carver
(played by Bruce Willis and Samuel L. Jackson) solve the two bucket variant
with two jugs and water from a public fountain in order to try to prevent a bomb
from exploding by obtaining 4 gallons of water using only 5-gallon and 3-gallon jugs.

General problems of this type are sometimes collectively known as "decanting problems."

Ball, W. W. R. and Coxeter, H. S. M. Mathematical
Recreations and Essays, 13th ed. New York: Dover, pp. 28 and 40, 1987.Bogomolny,
A. "3 Glasses Problem in Barycentric Coordinates." http://www.cut-the-knot.org/triangle/glasses.shtml.Bogomolny,
A. "Three Jugs Problem." http://www.cut-the-knot.org/ctk/Water.shtml.Bogomolny,
A. "Two Pails Puzzle." http://www.cut-the-knot.org/ctk/CartWater.shtml.Boldi,
P.; Santini, M.; and Vigna, S. "Measuring with Jugs." Theoret. Comput.
Sci.282, 259-270, 2002.Coxeter, H. S. M. and Greitzer,
S. L. "The Three Jug Problem." §4.6 in Geometry
Revisited. Washington, DC: Math. Assoc. Amer., pp. 89-93, 1967.Dudeney,
H. E. Amusements
in Mathematics. New York: Dover, p. 109, 1970.Eddy, R. H.
and Fritsch, R. "The Conics of Ludwig Kiepert: A Comprehensive Lesson in the
Geometry of the Triangle." Math. Mag.67, 188-205, 1994.Hegde,
S. M. and Kulamarva, S. "A Graph-Theoretic Model for a Generic Three Jug
Puzzle." 26 Aug 2023. https://arxiv.org/abs/2308.13868.McDiarmid,
C. and Ramirez Alfonsín, J. L. "Sharing Jugs of Wine." Disc.
Math.125, 279-287, 1994.O'Beirne, T. H. "Jug and
Bottle Department." In Puzzles
and Paradoxes. New York: Oxford University Press, pp. 49-75, 1965.Perel'man,
A. I. Zanumatel'naya Geometria. Moscow, 1958.Steinhaus,
H. Mathematical
Snapshots, 3rd ed. New York: Dover, pp. 61-63, 1999.Trott,
M. The
Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 104,
2004. http://www.mathematicaguidebooks.org/.Tweedie,
M. C. K. "A Graphical Method of Solving Tartaglian Measuring Puzzles."
Math. Gaz.23, 278-282, 1939.