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Walking On The Edge
How to use extreme way of thinking to tackle impossible questions
Consider the following example:
Two identical containers are each half filled with identical amounts of wine. One container is filled with red wine and the other with white wine. Using a third container, a certain amount of red wine is transferred from the red wine container to the white wine container and mixed. Using the same container, exactly the same amount of the white wine and the red mix is transferred back to the red wine container. What is there more, red wine in the white wine container or white wine in the red wine container?
Most of my students said that there is more red wine in the white wine container. Their explanation was that when the red wine was transferred, the third container contained only red wine, but on the way back it contained a mix of red and white. Their intuition when encountering this situation for the first time led them to a certain conclusion. When asked to prove their answer, most students started to plug in numbers just to find out it is not as simple as they thought. After experimenting with numbers for a few minutes almost all students return to their initial conclusion.
A good method that can be used to solve such a question is to use extreme situations. Since the size of the container used to transfer the wine was not defined in the question, it is possible to assume that any size we choose has to give the same result. Let’s begin by assuming it has a volume of zero. Hence, no red wine was transferred to the white container and no wine was returned. This makes the amounts equal (no red in the white and no white in the red). We can also assume the size of the third container was larger than each of the other two containers so all the red wine was transferred to the white. After mixing, the amounts of the red and the white are equal and they remain so when transferring the same amount back (since the concentration remains 50%). Again, the amounts are equal.
By looking at extreme situations (0 and 100%) it was possible to get to the right answer. Try this method on questions where a definition can fit many situations and plugging numbers does not help.
