You have five different jugs, without any marks at all, with capacities of 3, 4, 5, 6 and 7 litres. Initially, the 3, 5 and 7-jugs are completely filled with liquid (so we have 15 litres of the liquid; in the diagram below, an "x" stands for 1 litre) and the other two are empty. The jugs are arranged in the circular manner shown below, which can't be changed:

                           | |
                         +-+ +-+
                         | o o |
                         | o o | 
                         +-----+
              | |                        | | 
            +-+ +-+                  +---+ +---+
            |  x  |                  | x x x x |
            | x x |                  |  x x x  |
            +-----+                  +---------+

                   | |           | |                   
                +--+ +--+     +--+ +--+
                | x x x |     | o o o |
                |  x x  |     | o o o |
                +-------+     +-------+

The goal is to achieve 3 litres in each of the 5 jugs, only by pouring liquid from one jug into an adjacent one. (That is, at any time, you can pour liquid from the 3-jug only into the 4-jug or to the 5-jug; or from the 7-jug only into the 4-jug or to the 6-jug, etc...)

3 0 7 0 5
3 4 3 0 5
3 4 0 3 5
3 0 4 3 5
0 3 4 3 5
3 3 4 3 2
3 0 7 3 2
0 3 7 3 2
2 3 7 3 0
3 2 7 3 0
0 2 7 3 3
2 0 7 3 3
2 4 3 3 3
3 3 3 3 3

Posted by anubhav on 2005-08-23 01:49:49