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1. She would simply say "Nai (yes)" or "Ohkee (No)" and not announce the number of men who were adulterers nor would she identify them.

2. Also, if she arrived and made her announcement, the women would have to follow a particular rule. Once, the Oracle has announced her answer, if on any day a lady figured out that her husband was an adulterer, she would throw him out of the house the very next day at noon.

Now, the entire episode would be visible to every inhabitant of Potidaea. Also, every woman already knew what every man, other than her husband, was up to. However, she could not reveal that information to any other woman. Also, obviously, a cheating husband would not reveal his infidelity.

When the Oracle visited, she just said, "Nai" and left immediately. At noon on the 15th day after the Oracle left, for the first time, some women threw their husbands out of their homes. How many men were thrown out?

Detailed explanation along with Answer:

1. 15 men.

Case 1: One cheating husband
If only one man were cheating, his wife would easily work this out on the first day as she would have known that no other husbands were cheating and so the cheating husband must be hers.

Case 2: Two cheating husbands
Consider this from the point of view of Mrs. B, one of the wives (B and A) who were being cheated on, though all their positions are, in fact, the same. B would be aware that A's husband was cheating on her and would therefore expect that she would deduce this on the first day as in the example above. As, this does not happen B knows that A also is aware of a cheating husband. Since B was not aware of this, it has to be her husband who is cheating. A will go through the same thought process and so two men will be thrown out on the 2nd day.

Case 3: Three cheating husbands
C would be aware of A's and B's cheating husbands and expect the process to be solved as in the example above on the 2nd day. When this didn't happen, she would know that A and B must also be aware of 2 cheating husbands and will hence throw her husband out on the third day. A and B would do the same.

Case 4: N cheating husbands
Any of the wives being cheated on will be aware of N-1 cheating husbands and expect the process to be solved on the (N-1)th day. When this doesn't happen, they all become aware that all the other wives that they thought were being cheated were all under the same impression and hence they must be the Nth cheated on wife. Hence on the Nth day, N wives throw out N husbands.

Hence, on the 15th day, 15 men are thrown out.

Concluded.

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