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Morgan Stanley Induction Logic Interview Puzzle

Morgan Stanley Induction Logic Interview Puzzle - 23 December

The wisest men of the kingdom are called upon by the king to his court. One of them is to be chose for the advisor rank and thus they shall prove their worth in the test. The king places hat on each of their hats. Each one of them can see other two hats but can’t see his own. The hats are either white or black.

For a hint, the king tells them that at least one of them is wearing a black hat. Also the king declares that the test is totally fair for each one of them. Now the first one from them who is able to deduce the color of hat he is wearing will be designated as the advisor. After a few minutes, one of them was able to deduce the color of his own hat. How ?

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  1. They are both wearing black hats.
    If either scholar saw that the other one had a white hat, they could deduce they themselves had a black hat as they know at least 1 of them does. The scholar that wins notes that the other scholar does not immediately have this conclusion and therefore he must not have a white hat, as the game would already be over. From that it can be deduced that they both are wearing black hats, which is also whythe game is considered fair.

  2. I think its 3 people because it says "other two hats".. Still all 3 wear black hats .. because ww(b) is unfairly advantageous for (b) and wb(b) is unfairly advantageous for (b) [because wbw is not possible by earlier deduction]
    so only bbb is fair for all 3..