Solution:

At every floor, the detective had to open the window himself. If the man had committed suicide, then at least one of the windows must have been open. A person who is committing suicide won’t close the window behind him. Thus he knows that someone pushed him off the edge and closed the window afterwards.

Solution:

There are two things to keep in mind:
Firstly there is at least one red hat. (There can be two or three as well).
Secondly the competition is fair for everyone.

Thus if there is only one red hat, that person will see two green hats on other heads and will be able to deduce his own color as red. However the other students will see one red and one green hat and can never be sure. In such manner, the competition will prove to be partial for one student.

Suppose if there are two red hats. Then the students who are wearing red hats will see one red and one green hat on others. Now they must have deduced that there can’t be just one red hat. Thus they will know that they are also wearing a red hat. But the one who is wearing a green hat will see two red hats and can never be sure of his own color. In this case as well, the competition will not be fair.

Thus the only possible and fair means is if all of them are wearing a red hat. The one who is able to deduce the situation first, will raise his hand and will tell the correct answer.

Solution:

7.5Km

Explanation:
Denoting Ashley with A and Cecelia with C

Speed A = 60 km/hr = 1.2 x Speed C [km/hr] = 1 km/ min

Hence Speed C = 60/1.2 [km/hr] = 50 [km/hr] = 5/6 km/ min

Time C = D [km] /Speed C [km/min] = D/Speed C [min] = D/(5/6) min = 6D/5 min = 1.2 D min

Time A = D [km] /Speed A [km/min] = D/Speed A [min] = D/(1) min = D min

Since Time C – Time A = 1.5 min

Then (1.2 – 1)D min = 0.2D min = 1.5 min



Hence D = 1.5/0.2 km = 1.5*5 = 7.5 km

The total distance as calculated above is 7.5 Km.

Solution:

mother

We know from (3) that the youngest person was not the victim, from (4) that the youngest person was not the helper and from (6) that the youngest person was not the killer. The youngest person can only have been the witness therefore. If we make up a chart there are now three possible combinations:

Oldest person (father) H H M

Next to oldest (mother) V M H

Next to youngest (son) M V V

Youngest (daughter) W W W

(H = Helper ; V = Victim ; M = Murderer ; W = Witness)

We can work out from (5) that the father was the oldest, from (2) that the youngest person must have been the daughter. Therefore the next to the youngest must have been the son and the next to the oldest, the mother.

Solution:

Daniel Agger, Steven Gerrard, Nuri Sahin, and Raheem Sterling stated a contradiction statement, so only one of them can said the truth.
We don't know yet where Luis Suarez stands, it's still possible that he has black or white color.
Thus, the maximum possibility of white dots are 2, that is Luis Suarez and 1 of Daniel Agger Steven Gerrard Nuri Sahin, and Raheem Sterling.
Daniel Agger and Raheem Sterling obviously told the lie, as they said there are 3 and 4 person has white dot, which leave us Steven Gerrard and Nuri Sahin .
Assuming Steven Gerrard is white, then he must be telling the truth that he saw 4 black dots, which makes Nuri Sahin a liar. This is an impossible situation, since Nuri Sahin saw 3 black and 1 white (Nuri Sahin has to be a liar, so there must be more than 1 white, meaning it's impossible Steven Gerrard saw 4 blacks).
The only possibility is Nuri Sahin told the truth.
So, Daniel Agger Steven Gerrard Raheem Sterling have black dots, while Nuri Sahin and Luis Suarez have white dots.

Solution:

If two widows, each having a son married the son of the other widow, and then by the consummation of marriage, both the couples had a daughter, all the aforementioned relationships will turn to be true.

Solution:

The youngest son went over and blew out the candle after Death left because the son said 'till the candle wick burns out', not 'till the candle burns out'.

Solution:

Dabid is the killer

drawing room(D) , art room(a) , bed room (b) , ice-cream room (i) , desk room (d)

Solution:

The man said, 'I will be killed by giving poison.'

If Akbar says the statement is true, the man will be killed by hanging which will make his statement false.
If Akbar says the statement is false, the man will be killed by giving poison which will make the statement true.

Thus Akbar had no choice but to leave the man unpunished.

Solution:

You should choose the second shop.

It's a common logic. In the first shop, the barber had neat hairs. Since there are only two barbers in the entire town, he must have got his hairs cut from the barber in the second shop.