Question 1 -->Josephine
The recent expedition to the lost city of Atlantis discovered scrolls attributed to the great poet, scholar, philosopher Josephine. They number eight in all, and here is the first. The kingdom of Mamajorca, was ruled by queen Henrietta I. In Mamajorca women have to pass an extensive logic exam before they are allowed to get married. Queens do not have to take this exam. All the women in Mamajorca are loyal to their queen and do whatever she tells them to. The queens of Mamajorca are truthful. All shots fired in Mamajorca can be heard in every house. All above facts are known to be common knowledge. Henrietta 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. Queen Henrietta I is revered in Mamajorcan history.
ans-->>The two questions were:
1. How many husbands were shot on that fateful night?
2. Why is Queen Henrietta I revered in Mamajorca?
The answers are:
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 everyone has perfect information about everything except the fidelity of their 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. Now, imagine 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 n'th midnight.

Question 2 -->Belt
A magic rectangular belt always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface was 4 cm2. What was the original length, if the original width was 9 cm?
ans-->> The original length of belt was 96 cm.

Question 3 -->Aeroplane
There is only one airport on a fictional planet, and that is on the north pole. There are only 3 aeroplanes and lots of fuel at the airport. Full tank of an aeroplane lasts exactly to fly to the south pole, however the aeroplanes can transfer their fuel among one another. Your mission is to fly round the globe with at least one aeroplane (above the south pole) and in the end all aeroplanes must be OK back at the airport.
ans-->>Divide the way from pole to pole to 3 thirds (from the North Pole to the South Pole 3 thirds and from the South Pole to the North Pole 3 thirds).
1.2 aeroplanes to the first third, fuel up one aeroplane which continues to the second third and the first aeroplane goes back to the airport.
2.2 aeroplanes fly again from the airport to the first third, fuel up one aeroplane which continues to the second third and the first aeroplane goes back to the airport.
3.So there are 2 aeroplanes on the second third, each having 2/3 of fuel. One of them fuels up the second one and goes back to the first third, where it meets the third aeroplane which comes from the airport to support it with 1/3 of fuel so that they both can return to the airport. In the meantime, the aeroplane at the second third having full tank flies as far as it can (so over the South Pole to the last third before the airport).
4. The rest is clear – one (of the two) aeroplane from the airport goes to the first third (the opposite direction as before), shares its 1/3 of fuel and both aeroplanes safely land back at the airport.

Question 4 -->Reservoir
One reservoir has four taps. Using the first takes two days to saturate the reservoir, the second tap three days, the third four days and the last one 6 hours. What time will it last to fill the reservoir using all 4 taps at once?
ans-->>Because there are 24 hours in one day, in one hour fills the first tap 1/48, the second tap 1/72, the third tap 1/96 and the fourth tap fills 1/6 of the reservoir. That is all together (6+4+3+48) / 288 = 61/288. The reservoir will be full in 288/61 hours, which is 4 hours 43 minutes and about 17 seconds.

Question 5-->Clock
On every clock we can see that at noon the hour, minute and second hand correctly overlay. In about one hour and five minutes the minute and hour hand will overlay again. Can you calculate the exact time (to a millisecond), when it will occur and what angle they will contain with second hand?
ans-->>There are a few ways of solving this one. I like the following simple way of thinking. The given situation (when the hour and minute hands overlay) occurs in 12 hours exactly 11 times after the same time. So it’s easy to figure out that 1/11 of the clock circle is at the time 1:05:27,273 and so the seconds hand is right on 27,273 seconds. There is no problem proving that the angle between the hours hand and the seconds hand is 131 degrees.