You have 3 jugs of different size – 8 oz, 5 oz and 3 oz. Someone fills the 8 oz jug full of juice and you have to divide it exactly between two people – 4 oz in the largest (8 oz) jug, and 4 oz in the next largest (5 oz) jug – leaving the 3 oz jug empty. How can you solve this problem exactly, pouring the juice from jug to jug to arrive at the right quantities. (Note – you cannot just ‘estimate’ – you have to KNOW the quantities are exact).
Starting with the arrangement above you have to get to the arrangement below:
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Can you solve this problem better than I did? I simply (systematically) went through the ‘problem space’ of possible states, until I arrived at the answer. This is an excellent problem for getting across the important idea of a ‘problem space’ – the possible moves/states between start and goal, and how you can move deeper along certain paths in a problem space. Delineating problem spaces and then exploring them efficiently to find the goal state has to be central to many intelligent processes.
I did this with pen and paper, and thus the demands on my working memory were minimal. I wish I’d done this problem in my head to see how challenging it was. Much more interesting. Done this way, I believe that individuals with frontal lobe damage find the problem very difficult – in as far as they appear not to learn the moves to avoid, and they cycle through the same moves again and again, not coming closer to the goal state in the problem space. (Colvin et al. 2001).
Did this with pen and paper – having not done many explicit problems in the past 20 years I found it quite challenging but none the less fun. I went through the various movements of redistributing the volumes abd got there in about 7 moves bit it was more trial and error rather than working out the “system”
fun all the sane !
i like to think of “make a new number” to do it…