Puzzles/Action sequences/Barrel of Ale/Solution

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Puzzles | Action sequences | Barrel of Ale | Solution


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, empyting 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