Long Riddles With Answers

The police arrested Aman. This is because the numbers corresponds to the months.
8 - August
5 - May
4 - April
11 - November
Now taking the initials of the months, Aman is the name the victim was trying to tell.

Thursday.

Suppose that the person is speaking truth, he/she will have to lie on the next day but if he/she speaks lie by saying "Tomorrow I will lie.", then he/she will have to speak truth on the next day.

Thus, in each of the case, they will have to change their behavior the next day.

Now if you analyze, you will find out that Katniss can only say that statement on Thursday or Sunday. Peeta can say that statement on Monday or Thursday. Thus the only day common is Thursday.

This is possible if they were playing together as partners in a doubles match series.

(2^x)(30^3) = (2^3) (3^3) (4^3) (5^3)

(2^x)(30^3) = (120^3)

(2^x) = (120^3)/ (30^3)

(2^x) = (4^3)

(2^x) = 64

ln(2^x) = ln(64)

x ln(2) = ln(64)

x = ln(64)/ln(2)

x = 6

Thus x = 6.

43

You know that you can purchase any number of wings that is divisible by 3 but of course it should not be 3 itself. Thus, you should just try to purchase using the combinations of 9 and 6 boxes till the number is divisible by 3. If that number is not divisible by 3, then you have to use a box with 20. If the number that remains is divisible by 3, you are game. But if it is not divisible by 3, you can use a second box of 20. The number now will necessarily be divisible by 3.

Thus the largest number of wings that cannot be bought will come after buying two boxes of 20 and leaving a remainder that is divisible by 3:
3 + 20 + 20 = 43.

Palm Tree

infinite speed

Let us denote distance with d, time to get there by T, time to get back by t and the speed while travelling back with R.

Now by applying the simple time, distance and speed formula:
d = 20T
T = d/20

d = Rt
t = d/R

As you can see, we have the equations for both T and t now. We can now finally derive and equation for the round trip.

2d = 40(T + t)
2d = 40(d/20 + d/R)
2d = 40d(1/20 + 1/R)
1 = 20(R/20R + 20/20R)
20R = 20(R+20)
R = R + 20

You can clearly see that it is a paradox as to make the average speed 40 mph, you will have to travel back at an infinite speed. The faster you return, the quicker you can make it although your faster speed will offer a lesser impact on the average speed.

If you made the return trip instantly, it would be comparable to traveling double the distance in the same time that was taken on the one way trip.

Thus to reach the average speed of 40 mph, you must return with an infinite speed.

No excuse.
It signifies that there is no X listed.

B is speaking the truth.

A is lying when he says that B is lying. B is telling the truth when he says that C is lying. C is lying when he says that both A and B are lying since one of them is speaking the truth.

7
You must first divide the batteries in three groups: a group of two batteries and two groups of three batteries each. Now you have made sure that one of the group has two working batteries.

Now both the groups with three batteries can form three possible combinations and the group with two batteries has just one combination.

3 + 3 + 1 = 7.