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?

Charlie and his program came up with the same general solution as I.


A total of twenty-eight integral temperatures that can be obtained -- to include the two "do nothing" procedures to obtain containers of 50 and 90 degrees. As given by the following list, twenty-six other integral temperatures can be obtained, which include, each, a procedure to acquire the requested temperatures of 76 and 75 degrees.

A greater than sign (>) indicates the following container is filled as much as possible (i.e., without overflow) from the preceding container.  The 'x' following the given container indicates that container is emptied. I've left off the amount of water in each container, and, except for the final of that desired, the temperature of the water of each:

58. 5>3, 6>5, 5>6; 5x, 6>5, 3>6
60. 5>3, 5x, 6>5, 3>6
62. 6>3, 5>6, 6>5
63. 5>3, 6>5, 5>6, 5x, 6>5, 3>6, 6>3, 5>6, 6>5, 3>6
64. 6>3, 6x, 5>6, 3>5, 6>3, 3>5, 5>6, 6>3, 3>5
65. 6>3, 5>6, 6>5, 3>6, 6>3, 5>6, 3x, 5>3, 6>5, 3>6
66. 6>3, 5>6, 6>5, 5>6
67. 6>3, 6x, 5>6, 3>5, 6>3, 3>5, 5>6, 3x, 6>3, 3>5, 5>6
68. 6>3, 5>6, 6>5, 3>6, 6>3, 5>6, 3x, 5>3, 6>5, 3>6, 5>6
69. 6>3, 5>6, 6>5, 3>6, 6>3, 5>6, 3x, 5>3, 6>5, 3>6, 5>6, 6>3, 5>6, 3>6
70. 6>3, 5>6
71. 6>3, 5>6, 6>5, 3>6, 6>3, 5>6
72. 5>3, 6>5, 3>6, 6>3, 5>6
73. 6>3, 5>6, 5x, 6>5, 3>6, 6>3, 3x, 5>3, 6>5, 3>5
74. 5>3, 6>5
75. 6>3, 5>6, 5x, 3>5, 6>3, 5>6, 3>5, 6>3, 5>6
76. 6>3, 5>6, 5x, 3>5, 6>3, 5>6, 3>5, 6>3, 5>6, 3>5, 6>5, 6>3, 5>6, 3>5, 6>5
77. 6>3, 5>6, 5x, 6>5, 3>6, 5>6, 6>3, 3>5, 5>6
78. 5>3, 5x, 6>5, 3>6, 5>3, 5x, 3>5, 6>5
79. 6>3, 5>6, 5x, 6>5, 3>6, 6>3, 6x, 5>6, 3>5, 6>5
80. 6>3, 5>6, 6>5, 3>6
81. 5>3, 5x, 3>5, 6>3, 3>5, 5>6, 6>5, 3>6
82. 6>3, 5>6, 5x, 6>5, 3>6, 5>3, 5x, 6>5, 3>5
84. 6>3, 5>6, 6>5, 5>6, 5x, 6>5, 3>6
85. 6>3, 5>6, 5x, 6>5, 3>6
86. 5>3, 3x, 5>3, 6>5, 5>3, 3>6, 6>5

As can be seen from the list, I did not find solutions for temperatures less than 58 or greater than 86, nor for the intermediate 59, 61 or 83.

Edited on June 17, 2008, 5:51 pm

Posted by Dej Mar on 2008-06-17 17:47:02