Solution:

The woman started walking across the bridge when the guard was inside the hut. She walked all the time he was inside (5 minutes) and then turned and moved back towards the kingdom. On approaching the kingdom he was asked for papers and since she did not have any, she was sent back.

Solution:

This problem might seem complex but it can be solved completely using simple logics. We know that the bike is twice as fast as walking and thus the time taken by to reach hotel is equal to the time taken on foot to travel half the way. Thus, biking the whole way will be faster than taking the train if the train's speed is not infinite (not possible).

Solution:

301

= Explanation =
Time1 : When there are two pirates, 301/2 => remainder 1
Time2 : When there are three pirates, 301/3 => remainder 1
Time3 : When there are three pirates, 301/4 => remainder 1
Time4 : When there are three pirates, 301/5 => remainder 1
Time5 : When there are three pirates, 301/6 => remainder 1
Time6 : When there are three pirates, 301/7 => remainder 0

Solution:

Simple strategy: Elect one person to be the guesser, the other two pass. The guesser chooses randomly 'green' or 'blue'. This gives them a 50% chance of winning.


Better strategy: If you see two blue or two green hats, then write down the opposite color, otherwise write down 'pass'.

It works like this ('-' means 'pass'):

Hats: GGG, Guess: BBB, Result: Lose
Hats: GGB, Guess: --B, Result: Win
Hats: GBG, Guess: -B-, Result: Win
Hats: GBB, Guess: G--, Result: Win
Hats: BGG, Guess: B--, Result: Win
Hats: BGB, Guess: -G-, Result: Win
Hats: BBG, Guess: --G, Result: Win
Hats: BBB, Guess: GGG, Result: Lose

Result: 75% chance of winning!

Solution:

Ganpat had a black suit and a brown suit.
Harish had a brown suit and a pink suit.
Manoj had a white suit and a black suit.
Tarun had a pink suit and a white suit.

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.

Solution:

Let the length of the bridge be x meters.
Running towards the train, Charles covers 0.5x-10 meters in the time that the train travels x-4 meters. Running away from the train, Charles covers 0.5x+2 meters in the time that the train travels 2x-8 meters.

Because their speeds are constant, the following holds:

(0.5x-10) / (x-4) = (0.5x+2) / (2x-8)
which can be rewritten to
0.5x2 - 24x + 88 = 0
Using the abc formula we find that x=44, so the railway-bridge has a length of 44 meters.

Solution:

The code is 645
Explanation :
A) From Clues 1st and 2nd we know that one 9 is not in the code
B) From Clue 2nd we know that 9 3 and 8 are part of code
C) From Clue 3rd we know that 4 and 6 are part of code
D) From Clue 5th we know that 1 and 2 are not part of the code as we know 6 is part of the code and just 1 of 3 numbers is part of code.
E) From Clue 4th we know that 5 is also in the code as 8 and 1 are not part of code.

So the code is: 645

Solution:

Uncle Scrooge tells him he took the loan to keep his expensive car safe and he also saves money on security and parking rent.

Solution:

In such questions, the best thing is to assume each one of them as his sister till you can find all the conditions fulfilled. According to our assumptions, Megan is Alex's sister. We will discuss only this case therefore.

Assuming that Megan is Alex's sister, she has told a lie. This also means that Maggie is not Alex's girlfriend.
If Katie is the truth speaking girl, Megan is lying and it proves our assumption.
Now, if Charlize is Alex's girlfriend, she has also told a lie. This further tells that Katie is speaking the truth which also supports our assumption.
Maggie stated that Charlize is not his sister and that is also true because according to our assumption, Charlize is his girlfriend.

Taking that into account, we can conclude that Megan is Alex's sister and Charlize is his girlfriend.

In any other assumption, you will find the data conflicting with the conditions.