# 2 Pails Puzzle

(Two containers and a pond are depicted in the right-hand side of the applet. To pour water, first click on the "source" and then on the "receiver" object.

The grid in the left-hand side of the applet is to help you solve the problem.

- The Three Jugs Problem. Introduction and a story
- 3 Glasses Puzzle
- Water puzzle, experimental math
- Three Glass Puzzle (Graph Theoretical Approach)
- The puzzle in barycentric coordinates
- Two Pails Puzzle
**Plain Gadgets**- 3 Jugs Problem - A Water Doubling Variant

|Contact| |Front page| |Contents| |Algebra| |CTK|

Copyright © 1996-2018 Alexander Bogomolny

This puzzle is no different from the 3 Jugs Problem. Indeed, the problem with two containers of capacities 11 and 6 is the same as the problem with 3 containers of capacities 11, 6, and

From the analysis of the 3 Jugs Problem, we already know that the more general problem with integer capacities A and B always has a solution iff A and B are mutually prime.

However the argument there made a heavy use of the third quantity C - capacity of the third container. This is not necessary as we may directly work in Cartesian coordinates, instead of the barycentrics. Let *basic step* we consider pouring from the pond to B and from B to A. Sooner or later, A will become full, at which stage we apply the *secondary step* by emptying A into the pond and pouring the content of B into A. The secondary step is applied only when A becomes full. If *vector*

which, as we know, fills the entire set

In addition, once a quantity from the set

- The Three Jugs Problem. Introduction and a story
- 3 Glasses Puzzle
- Water puzzle, experimental math
- Three Glass Puzzle (Graph Theoretical Approach)
- The puzzle in barycentric coordinates
- Two Pails Puzzle
**Plain Gadgets**- 3 Jugs Problem - A Water Doubling Variant

|Contact| |Front page| |Contents| |Algebra|

Copyright © 1996-2018 Alexander Bogomolny

68861653