Solution:

2nd

When the cylinder is spun for the first and last time, the following six outcomes are possible:

First:
First chamber is fired first. The first player loses.

Second:
Second chamber is fired first. The first player loses.

Third:
Third chamber is fired first. The first player loses.

Fourth:
Fourth chamber is fired first. The second player loses. (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)

Fifth:
Fifth chamber is fired first. The first player loses. (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)

Sixth:
Sixth chamber is fired first. The second player loses. (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)

Thus, if you analyze, you will find that the second player has a 4/6 chance of winning. Therefore if you want to win the game, going second gives you better shot at it.

Solution:

No one understands

Solution:

Let us solve this problem with variables to find the general nature. Let us assume that there are x black chocolates and y white chocolates. Three things can happen when you take out two chocolates.
1) You take out two black chocolates.
Then, you will be replacing one black chocolate and so the jar will have x+1 black chocolates and y-2 white chocolates.
2) You take out two white chocolates.
Then, you will be replacing 1 black chocolate and so the jar will have x-1 black chocolates and y white chocolates.
3) You take out 1 black chocolate and 1 white chocolate. Then, you will be replacing a white chocolate and so the jar will have x-1 black chocolates and y white chocolates.
Thus at every step, you are wither removing a black chocolate or replacing two white chocolates by one black chocolate irreversibly till there is just one chocolate left. Therefore each white chocolate is equivalent to two black chocolates.

This, if the number of white chocolates are odd in number, the last one remaining will be white chocolate and if the number of white chocolates are even in number, the last one remaining will be black chocolate.

Solution:

The Pink servant is the truthful one.

In order to prove the same, let us take all of them one by one assuming that the selected one is telling the truth. This is because all of them are disagreeing with each other which means that three servants are lying while one is telling the truth.

Assume that the Orange servant is the truthful one. Under this condition, the orange one is having either 6 or 8 legs. And each of the other octopus is lying will then have 7 legs. Under this condition, the total number of legs will be 6 + 7 + 7 + 7 = 27 legs or 8 + 7 + 7 + 7 = 29 legs. But the Orange servant said that they have 28 legs all together. Thus he is lying.

Now if we simply follow the same logic with all other servants as well, we will come up to the conclusion that only the Pink servant is truthful.

Solution:

512

Explanation:
The cube that remains will be 8 x 8 x 8. This will make a total of 512. This is because, when a layer is taken, it will be taken from all sides of the cube which will reduce the dimension be two and not one.

Solution:

The main idea for getting the solution for this puzzle is that the pirate should know that he will be getting the treasure for the acceptance of the proposal. And if he gets to know that the treasure he is getting is less than the others then he will not accept the proposal. If the last one who is left is the pirate 1 then he will be the one who will be getting all the golden coins.


If pirate 1 would be the only one left, he would get all the golden coins. If only pirates 1 and 2 would be left, pirate 2 would die for sure, since pirate 1 is bloodthirsty and will reject all proposals of pirate 2 (since he will get all coins anyway). So:
| Pirate 1 | Pirate 2
----------------+------------+------------
Number of coins | 1000 | 0
----------------+------------+------------
Pirate agrees | No | Yes
When also pirate 3 would still be alive, he needs the agreement of one of the other two. Pirate 2 will agree with every proposal since, as we have seen, he would die if he did not. Therefore, pirate 3 should propose to keep everything for himself.
| Pirate 1 | Pirate 2 | Pirate 3
----------------+------------+------------+------------
Number of coins | 0 | 0 | 1000
----------------+------------+------------+------------
Pirate agrees | No | Yes | Yes
When we have four pirates, pirate 4 should make two other pirates agree with his proposal. Therefore, he proposes to give one coin to pirate 1, one coin to pirate 2, and the rest to himself. Pirates 1 and 2 will accept the proposal, since they are greedy, and if they would not accept, they would get less.
| Pirate 1 | Pirate 2 | Pirate 3 | Pirate 4
----------------+------------+------------+------------+------------
Number of coins | 1 | 1 | 0 | 998
----------------+------------+------------+------------+------------
Pirate agrees | Yes | Yes | No | Yes
However, as we know, there are five pirates. If pirate 5 gives both pirate 1 (or 2) and pirate 3 one coin more than in the previous case, they are willing to accept the proposal. Then a majority (three out of five) of the pirates will support the proposal, and pirate 5 can keep the rest of the treasure to himself.
| Pirate 1 | Pirate 2 | Pirate 3 | Pirate 4 | Pirate 5
----------------+------------+------------+------------+------------+------------
Number of coins | 2 | 0 | 1 | 0 | 997
----------------+------------+------------+------------+------------+------------
Pirate agrees | Yes | No | Yes | No | Yes
Conclusion: Pirate 5 should propose to give two coins to pirate 1 (or 2), one coin to pirate 3, and the remaining 997 coins to himself.

Solution:

Three options possible :

1. Father and child.
2. paternal uncle-aunt.
3. nephew and niece

Solution:

The color of the hat which the man A is wearing is the white color hat.
It is clear with the question and the clue itself that neither B nor C has information regarding this and therefore they do not answer. For the explanation, let's start from C. the man C can see man A's hat and also man B's hat. He must be seeing at least one white hat on any one of them. If he sees two black hats, then he clearly knows that he is wearing a white colored hat. But the man B cannot give an answer. He might see a white hat on man A. if the man B saw a black hat on A, he would know that he is wearing a white one. The question itself says that the man A answers to the question and therefore, the man A shouts that he is wearing a white one.

Solution:

3383

Explanation

Value of pi to 100 digits
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

and 264 are next four numbers.

Solution:

Let the distance between Peter's (hereafter referred as P) and Rhea's (hereafter referred as R) be D.
When P and R meet for the first time, P has traveled 500 miles.
In that case, R has traveled (D - 500) miles.
=> Speed of P / Speed of R = 500 / (D - 500) ...... (1)

When P and R meet for the second time, P has traveled (D - 500) + 300 miles
Now, R has traveled (500 + D - 300)
=> Speed of P / Speed of R = 5 / (D - 5) ..... (2)

Equating (1) and (2)
500 / (D - 500) = (D - 2) / (D + 2)
D = 1200 Miles.