You only have these three containers, all irregular in their shape (though it doesn´t appear in the simplified drawing below), with no marks in them, and all that you know is the capacity of each one.

The 3-liter is empty, the 5-liter is full of 50ºC water, and the 6-liter is full of 90ºC water.

                                  |/////|
                      |/////|     |/////|
                      |/////|     |/90º/|
          |     |     |/50º/|     |/////|
          |     |     |/////|     |/////|
          |     |     |/////|     |/////|
          +-----+     +-----+     +-----+
           3-lit       5-lit       6-lit

With a succession of moves, how do you get some water at 76ºC? At 75ºC?

How many different integral temperatures, from 50ºC to 90ºC, can you get?

Lacking the thouroughness of Charlie's computer algorithm, I had only found: 58, 60, 62, 66, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 82, 84, 85, and 86.   Of those, 77 is the most complicated.

 

Posted by Leming on 2008-06-17 16:50:29