Hard Riddles

The elf Ee should give 997 coins to himself, 2 coins to either Elf Aye or Bee, and 1 coin to Cee.
Here, we derive the solution working backwards.
If only elf Aye and Bee are left, Aye will reject all proposals from Bee, since elves are greed and killers, as Aye gets to keep all 1000 coins.
However, if Cee was alive, and would give 1000 coins all to himself, even then Bee would agree since If he does not, Cee dies, and as we have seen, if only Aye and Bee are left, Bee will be killed. So the vote is Aye: No, Bee and Cee, yes.
Now if Dee was alive, he would propose to give 1 coin to Aye, 1 to Bee, none to Cee and 998 to himself. Aye and Bee will agree to this, because if they dont, Dee will die and Cee will get to keep all 1000 coins. Since they are greedy, and would prefer 1 coin over none, they will agree to this proposal.
However, elf Ee should give 2 coins to Aye (so he will agree as he gets 1 extra coin over the previous proposal). He will give 0 coins to Bee. He shall give 1 coin to Cee (and Cee will agree since in the previous proposal, Cee was getting nothing). He will give Dee 0 coins so D will disagree. Obviously, Ee gives himself 997 coins. The vote is 3 yes, two nos. Thus Ee will propose this.

megalomaniac. (Camel , Main and Ago)

Following Options possible

(A) Father and child.
(B) paternal uncle-aunt.
(C) nephew and niece

Man 1 is wearing white. He arrives at the conclusion as follows:
From the fact that neither 2 nor 3 gives the answer, 1 concludes that both these men have insufficient information to determine the color of their hats.
Man 3 must be seeing at least one white hat on the heads of 1 and 2 (if he would see two black hats, he would know that he is wearing a white hat). Further, Man 2 therefore knows that he and/or A is wearing a white hat. Since he cannot give an answer, he must be seeing a white hat on 1st head (if 2 would see 1 wearing a black hat, he would know that he himself wears a white one). From the fact that neither 2 nor 3 can give an answer to the riddler question, 1 finally concludes that he is wearing a white hat! He thus shouts the correct answer and all 3 of them are released. Yay.

264

The value of pi to 100 digits is
1415926535897932384626433832795028841971693993751058209749445923078164
062862089986280348253421170679

3.75

This question can be solved mathematically.
Let us assume that the initial amount of petrol is p.
The time for which they drove be t.
Now, the amount of petrol used by one car in t hours will be = pt / 4
The amount of petrol used by the second car in t hours will be = pt / 5
Now, the petrol left in the first car will be = (p - pt / 4)
The petrol left in the second car will be = (p - pt / 5)
According to the question
P - pt / 5 = 4(p - pt / 4)
T = 15 / 4 or 3.75 hours.
Therefore, both of the friends have driven the car for 3.75 hours.

Let us assume that the distance between P house and Q house be D.
Upon their first meet, P has traveled 500 yards.
Thus the distance traveled by Q = D - 500.
Calculating D as a multiple of 100 to simplify the equation
=> Speed of P / Speed of Q = 5 / (D - 5)..... (a)

Upon their next meet, P has traveled (D - 500) + 300
Distance traveled by Q = 500 + D - 300
=> Speed of P / Speed of Q = (D - 2) / (D + 2) ..... (b)

When we equate (a) and (b)
5 / (D - 5) = (D - 2) / (D + 2)
D = 12

Therefore, the distance between P and Q house is 1200 Yards.

141

Its a sequence on prime number(post number 100) + 10.
7 prime number after 100 are listed below.
101 , 103 , 107 , 109 , 113 , 127 , 131

Our solution is 131+10 => 141

Both A and D will rotate at Same speed. Gears of the equal size will rotate at constant speeds despite or any sized gears in between them.

One for all or all for one.