Solution:

Suppose if there is just one unfaithful husband, then his wife will kill her husband as she must be knowing that all other men are faithful but the queen declared that one of them all is unfaithful.

If there are two unfaithful husbands, then both their wives will believe there is just one unfaithful husband, that too the other one whom she knows. Thus both of them will expect the above case to happen at midnight. But when no one is shot, they will realize that there are two unfaithful husbands and since they know about everyone, they will know that the other unfaithful man is their own husband on the next day.

If there are three unfaithful husbands, each of their wives will be knowing about two other unfaithful men so they will be expecting the above case and will be waiting for the gunshots on the second day. When that does not happens, they will realize that there are more than two and since they all will know about the rest, they will realize that their own husband is unfaithful and they will kill him on the third day.

Thus if we talk about general terms and suppose that there are n unfaithful husbands, their wives will believe that there is n-1 unfaithful husbands and will expect the gunshot on n-1 day. When they don’t hear that, they will realize their own husband is the nth.

Solution:

The teacher will use a simple trick to form a perfect impression. He will ask all his students to raise their hands on each of the question that is asked. But the only catch will be that those who knows the answer correctly will raise their right hand and others will raise their left hand.

In this way, the principal will see all the hands being raised for each question even though all won't be knowing the correct answer. The teacher will ask only those who know the answer and they will always be correct. So the principal will be impressed to full extent.

Solution:

When you were inside the shed, the murderer replaced the lock with his own one that was identical to your original lock. When you locked the store room, you did not require a key and there was nothing abnormal for you. When you left, the murderer opened the lock with his key, planted the dead body inside and replaced the lock again putting the original lock in the place. He then closed it without any problem.

Solution:

He simply suggested that one of the brothers will be allowed to divide the land but he must take into consideration that it will be the other one who will have a choice of selecting his land between the two halves first.

Thus both will be happy in such manner.

Solution:

Move the coins as given in the figure and you will get the required result.

Solution:

David to play second

Explanation:
Let's suppose that David plays first and he picks 9. Then Albert will definitely pick 8. Now, David will have to pick 7 or Albert will pick 7 in his turn. But if David picks up 7, then he will score 16 that is beyond 15 and will lose. So one thing is for sure, no one will be willing to start with the highest digits.

Suppose David plays first and picks up 1, Albert will pick 2. Then David will pick 3 and Albert will pick 4. Now David will be forced to pick 9. The score is 6 to 13 and thus David will have no chance of winning.

If David Picks 9 after Albert has picked up 2, then Albert will pick 8 and the score will become 10 to 10. Thus David will pick 3 as picking 7 will send him past 15. Now Albert will pick 4 and David has nothing to pick for winning. Thus Albert wins.

Therefore, you should suggest David to play second.

Solution:

8/(1−1/5)

Solution:

Here is a way to do it. We dont know if it can be done using some other arrangement or not. If you know, do send us.

4 | 3 | 8
9 | 5 | 1
2 | 7 | 6

Solution:

The figure tells that B is located to the North-East of E.

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

Now there can be two solutions to the given situation because there can be two situations:
Suppose if B and C have same colors, A will know that his color is the other one and he will be able to speak up the first.
Now if B and C do not have same colors, A will stay silent. This will tell B that his and C's colors are different. Thus he will speak up first.

So either A or B will speak up first depending on the situation.