You have two containers with capacities a = 5, b - 3 liters. The objective is to

Question

You have two containers with capacities a = 5, b - 3 liters. The objective is to obtain exactly c liters into one of the containers. You can only perform the following operations: Fill a container to the top, Empty a container completely, Pour the liquid from one container to the other. Describe how to solve the "Die Hard" problem when a = 5, b = 3 and c - 4. How do you solve the problem if c = 1? Discuss how to solve the problem when a - 12, b - 9 and c = 4. Describe the condition required of a and b so that you can always solve the problem for any max(a, b)?

Explanation / Answer

Question A) Answer is below Picture

The above solution when a = 5, b =3 and c = 1

Question B) Answer is below Picture

The above solution is

When a = 5, b = 3 and c = 4

Question B) When A =12, B= 9 and C = 4
Amount After Action                             Action             

12 -Leters jug         9-Leters Jug
       0                    9                 Fill 9-Leters Jug
       9                    0                 Transfer from 9 to 12 leters jug
       9                    9                 Fill 9-leters Jug
       12                   7                 Transfer 3-leters from 9-leters jug to 12-leters
       0                    7                 Empty 12-leters jug
       7                    0                 Transfer 7-leters from 9-leters jug to 12-leters
       7                    9                 Fill 9-leters jug
       12                   4                 Transfer 5-leters from 9-leters jug to 12-leters
       0                    4                 Empty 12-leters jug, so 9-leters jug have 4-leters

Question C Answer :

The more general problem is finding integer solutions for the equation ax + by = c. Solutions (x,y) exist when the greatest common divisor of a and b is a factor of c. This is an ancient problem. For more, read this article: http://mathforum.org/library/drmath/view/51595.html

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