Puzzles/Action sequences/Barrel of Ale/Solution

Puzzles | Action sequences | Barrel of Ale | Solution

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There are 6 operations that can be done in any order to arrive at one pint. These are: Filling the 5 pint mug, filling the 3 pint mug, pouring the contents of the 5 pint mug into the 3 pint mug, pouring the contents of the 3 pint mug into the 5 pint mug, emptying the 3 pint mug (presumably by drinking it), and emptying the 5 pint mug. Using these operations, there are two ways to arrive at 1 pint.

	5 Pint Mug	3 Pint Mug
1	5	0
2	2	3
3	2	0
4	0	2
5	5	2
6	4	3
7	4	3
8	4	0
9	1	3

Or, much more quickly:

	5 Pint Mug	3 Pint Mug
1	0	3
2	3	0
3	3	3
4	5	1