Angoel (angoel) wrote,

One of the features of visiting the group of friends in Oxford whom I spent my weekend with, is that they invariably pass on a logical problem that they're attempting to solve. One of the those this weekend was a particularly nice variant on the old 'two guards' chestnut.

"There are three oracles, who will answer yes-no questions with absolute accuracy. However, they don't necessarily answer the questions that you have asked them:

o the oracle of the past answers the previous question put to one of the oracles
o the oracle of the present answers the current question put to one of the oracles
o the oracle of the future answers the next question which will be put to one of the oracles

You don't know which of the three oracles is which, and wish to find out. To this end, you may ask three questions of the oracles. Is it possible to work out which is which, and if so, how?

[To prevent paradoxes with the oracle of the future, the questions should be predetermined, however the choice of which oracle to ask each question does not have to be. If you still insist on causing a paradox, the gods will smite you for being cheeky; don't do that.]

[If you ask the oracle of the past your first question, he will answer the question put to him by the previous petitioner. If you ask the oracle of the future your third question, it will answer the question put to it by the next petitioner. In each of these cases, the answers are effectively random.]

[There were some other restrictions about not having questions which referred to other questions, presumably to stop you gaming the puzzle in certain ways. I broadly interpreted those as 'stop buggering about and ask straightforward questions', and thence ignored them, so I can't tell you exactly what they were.]"

There's an interesting related problem it which you're still trying to identify the oracles, in which all three oracles answer the question put to them (subject to their vagueries about which question has been asked) but you only can put two questions to them. I'm still working on that one...
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