What satisfies these five conditions?

* Beelzebub says there's a small problem here. If God is omniscient SHE can see every event in the future. But then she can't be omnipotent and change events in the future. Similarly, if SHE is omnipotent she can alter the future at will so She can't be omniscient.

PROBLEM 2

The recent expedition to the lost city of Atlantis discovered scrolls attributed to the great poet, scholar, philosopher Josephine. They number eight in all. Here is the first.

The kingdom of Mamajorca, was ruled by truthful Queen Henrietta I. In Mamajorca all women except the Queen have to pass an extensive logic exam before they are allowed to get married. All the women in Mamajorca are loyal to their Queen and do whatever she tells them to do. All shots fired in Mamajorca can be heard in every house. All the above facts are common knowledge.

Unmarried Henrietta was a killjoy and, accordingly, was worried about the infidelity of the married men in Mamajorca. She summoned all the wives to the town square, and made the following announcement. "There is at least one unfaithful husband in Mamajorca. All wives know which husbands are unfaithful, but have no knowledge about the fidelity of their own husband. You are forbidden to discuss your husband's faithfulness with any other woman. If you discover that your husband is unfaithful, you must shoot him at precisely midnight of the day you find that out."

Thirty-nine silent nights followed the Queen's announcement. On the fortieth night, shots were heard.

1. How many husbands were shot on that fateful night?

2. How did their wives deduce their unfaithfulness?

1) Nothing.

2) If there are n-unfaithful husbands (UHs), every wife of an UH knows of n-1 UH's while every wife of a faithful husband knows of n UHs. [this because each woman has perfect information about husband infidelity except the fidelity of her own husband. Now we do a simple induction: Assume that there is only one UH. Then all the wives but one know that there is just one UH, but the wife of the UH thinks that everyone is faithful. Upon hearing that "there is at least one UH", the wife realizes that the only husband it can be is her own, and so shoots him at midnight. Next assume that that there are just two UH's. Each wife of an UH assumes that the situation is "only one UH in town" and so waits to hear the other wife (she knows who it is, of course) shoot her husband on the first night. When no one is shot, that can only be because her OWN husband was a second UH. The wife of the second UH makes the same deduction when no shot is fired the first night (she was waiting, and expecting the other to shoot, too). So they both figure it out after the first night, and shoot their husbands the second night. It is easy to tidy up the induction to show that the n UHs will all be shot just on the nth midnight.

N.B. This was originally heard about "unfaithful wives." However, for the sake of safety in these PC days, I have switched genders. [only kidding!!!]

- Jer