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Puzzles

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Classic Five-Hat Problem (Answer)
Oil and Vinegar Problem (Answer)
Game Show Problem (Answer)

Let us call the volume of a spoonful x and the amount of oil contained in the spoonful transferred from the vinegar y. The volume of vinegar transferred to the oil is therefore (x-y), and the net volume of oil transferred to the vinegar is also (x-y). So neither liquid is more contaminated than the other.


I first heard this problem more than forty years ago, proposed by Edward de Bono. I got the answer wrong and de Bono told us that people of Western culture generally did, but that people with other cultural backgrounds were not confused by the problem. When I was studying with students from various backgrounds, I thought I would test this assertion. The results of my investigation appeared to bear it out.

The white British students gave the same answer as I had.
A Sinhalese-speaking Buddhist student immediately replied, "They are both the same."
I asked two Gujarati-speaking Ismaili Moslem students from East Africa. One raised objections, assuming there was a catch, and could not get further than the problem of miscibility. The other did not understand the proposition and did not answer.
A Catholic Goan student educated first in India, then in East Africa, gave the Western answer.

Obviously, the sample was very small, but my findings were, as far as they went, consistent with the assertion.


Some years later I tried the problem on a Scottish colleague who is probably the most intelligent person I have ever known. I would sometimes use his brain as a short cut to the answers to logical problems with which I was having trouble. He immediately replied, "Instinctively I'd say they're both the same, but let's work through it logically." He then proceeded to demonstrate that he was right.


Oh by the way, I didn't say what the "Western answer" is. Well, Westerners think about the whole spoonful of oil going to the vinegar and the partial spoonful of vinegar going to the oil, but forget about the oil that goes back again. So they say, as I did, that there is more oil in the vinegar than vinegar in the oil.


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