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Question
Decanting problem. You are given three bottles of capacities 5,8 and 3 litres. The 8L bottle is filled with oil, while the other two are empty. Divide the oil in an 8L bottle into two equal quantities. Represent the state of the process by appropriate variables. What are the initial and final states of the process? Model the decanting of oil from one bottle to another by assignment. Write a sequence of assignments to achieve the final state.
Solution
To divide the oil equally in the oil bottle, the following 7 steps are needed:
- Pour 5L of oil into the second bottle. (3,5,0)
- Pour 3L from the second bottle to the third. (3,2,3)
- Pour 3L from the third to the first. (6,2,0)
- Pour all 2L from the second to the third bottle (6,0,2)
- Pour 5L from the first to the second bottle. (1.5.2)
- Pour 1 L from the second to the third bottle. (1.4.3)
- Finally, pour now all 3L from the third bottle to the first (4,4,0)
Assignment statement as follows:
- E,F,T = 8,0,0
- E,F,T = 3,5,0
- E,F,T = 3,2,3
- E,F,T = 6,2,0
- E,F,T = 6,0,2
- E,F,T = 1,5,2
- E,F,T = 1,4,3
- E,F,T = 4,4,0
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